CAT Triangles Practice Questions With Solutions

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CAT Quant Triangles Practice Questions

VARC DILR

Question 1.

A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio a : b. If the radius of the circle is r, then the area of the triangle is

$\frac{abr^{2}}{2(a^{2}+b^{2})}$

$\frac{2abr^{2}}{a^{2}+b^{2}}$

$\frac{4abr^{2}}{a^{2}+b^{2}}$

$\frac{abr^{2}}{a^{2}+b^{2}}$

Question 2.

Let $\triangle ABC$ be an isosceles triangle such that AB and AC are of equal length. AD is the altitude from A on BC and BE is the altitude from B on AC. If AD and BE intersect at O such that $\angle AOB = 105^\circ$ , then $\frac{AD}{BE}$ equals

$\sin 15^\circ$

$\cos 15^\circ$

$2 \cos 15^\circ$

$2 \sin 15^\circ$

Question 3.

The length of each side of an equilateral triangle ABC is 3 cm. Let D be a point on BC such that the area of triangle ADC is half the area of triangle ABD. Then the length of AD, in cm, is

$\sqrt{8}$

$\sqrt{6}$

$\sqrt{7}$

$\sqrt{5}$

Question 4.

In a triangle ABC, AB = AC = 8 cm. A circle drawn with BC as diameter passes through A. Another circle drawn with center at A passes through Band C. Then the area, in sq. cm, of the overlapping region between the two circles is

$16\pi$

$16(\pi - 1)$

$32(\pi - 1)$

$32\pi$

Question 5.

Two ships are approaching a port along straight routes at constant speeds. Initially, the two ships and the port formed an equilateral triangle with sides of length 24 km. When the slower ship travelled 8 km, the triangle formed by the new positions of the two ships and the port became right-angled. When the faster ship reaches the port, the distance, in km, between the other ship and the port will be

Question 6.

The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side. P is the midpoint of CD and ABPD is a parallelogram. If the difference between the areas of the parallelogram ABPD and the triangle BPC is 10 sq cm, then the area, in sq cm, of the trapezium ABCD is

Question 7.

If a triangle ABC, $\angle BCA=50^{0}$ . D and E are points on $AB$ and $AC$ , respectively, such that $AD=DE$ . If F is a point on $BC$ such that $BD=DF$ , then $\angle FDE$ , in degrees, is equal to

100

Question 8.

Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to

8.8

7.8

6.6

7.2

Question 9.

The sum of the perimeters of an equilateral triangle and a rectangle is 90cm. The area, T, of the triangle and the area, R, of the rectangle, both in sq cm, satisfying the relationship $R=T^{2}$ . If the sides of the rectangle are in the ratio 1:3, then the length, in cm, of the longer side of the rectangle, is

Question 10.

From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is s. Then the area of the triangle is

$\frac{\sqrt{3}s^{2}}{2}$

$\frac{2s^{2}}{\sqrt{3}}$

$\frac{s^{2}}{2\sqrt{3}}$

$\frac{s^{2}}{\sqrt{3}}$

Great Job! continue working on more practice questions?

Question 1.

The vertices of a triangle are (0,0), (4,0) and (3,9). The area of the circle passing through these three points is

$\frac{14\pi}{3}$

$\frac{123\pi}{7}$

$\frac{12\pi}{5}$

$\frac{205\pi}{9}$

Question 2.

AB is a diameter of a circle of radius 5 cm. Let P and Q be two points on the circle so that the length of PB is 6 cm, and the length of AP is twice that of AQ. Then the length, in cm, of QB is nearest to

9.3

7.8

9.1

8.5

Question 3.

In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, is

2.5

1.5

3.5

0.5

Question 4.

If the rectangular faces of a brick have their diagonals in the ratio $3 : 2 \surd3 : \surd{15}$ , then the ratio of the length of the shortest edge of the brick to that of its longest edge is

$\sqrt{3} : 2$

$1 : \sqrt{3}$

$2 : \sqrt{5}$

$\sqrt{2} : \sqrt{3}$

Question 5.

The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length of each side being 20 cm. The vertical height of the pyramid, in cm, is

$10\surd2$

$8\surd3$

$5\surd5$

Question 6.

Let ABC be a right-angled triangle with hypotenuse BC of length 20 cm. If AP is perpendicular on BC, then the maximum possible length of AP, in cm, is

$8\surd2$

$6\surd2$

Question 7.

In a triangle ABC, medians AD and BE are perpendicular to each other, and have lengths 12 cm and 9 cm, respectively. Then, the area of triangle ABC, in sq cm, is

Question 8.

Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3,... will be

$188\sqrt{3}$

$248\sqrt{3}$

$164\sqrt{3}$

$192\sqrt{3}$

Question 9.

In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm, respectively. Let P be a point on CD such that AP is perpendicular to CD. Then the area, in sq cm, of triangle APD is

$32\sqrt{3}$

$18\sqrt{3}$

$24\sqrt{3}$

$12\sqrt{3}$

Question 10.

A triangle ABC has area 32 sq units and its side BC, of length 8 units, lies on the line x = 4. Then the shortest possible distance between A and the point (0,0) is

$8$ units

$4$ units

$2\sqrt{2}$ units

$4\sqrt{2}$ units

Great Job! continue working on more practice questions?

CAT Triangles Practice Questions With Solutions

CAT Quant Triangles Practice Questions

Question 1.

A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio a : b. If the radius of the circle is r, then the area of the triangle is

Question 2.

Let △ABC\triangle ABC△ABC be an isosceles triangle such that AB and AC are of equal length. AD is the altitude from A on BC and BE is the altitude from B on AC. If AD and BE intersect at O such that ∠AOB=105∘\angle AOB = 105^\circ∠AOB=105∘, then ADBE\frac{AD}{BE}BEAD​ equals

Question 3.

The length of each side of an equilateral triangle ABC is 3 cm. Let D be a point on BC such that the area of triangle ADC is half the area of triangle ABD. Then the length of AD, in cm, is

Question 4.

In a triangle ABC, AB = AC = 8 cm. A circle drawn with BC as diameter passes through A. Another circle drawn with center at A passes through Band C. Then the area, in sq. cm, of the overlapping region between the two circles is

Question 5.

Question 6.

The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side. P is the midpoint of CD and ABPD is a parallelogram. If the difference between the areas of the parallelogram ABPD and the triangle BPC is 10 sq cm, then the area, in sq cm, of the trapezium ABCD is

Question 7.

If a triangle ABC, ∠BCA=500\angle BCA=50^{0}∠BCA=500. D and E are points on ABABAB and ACACAC, respectively, such that AD=DEAD=DEAD=DE. If F is a point on BCBCBC such that BD=DFBD=DFBD=DF, then ∠FDE\angle FDE∠FDE, in degrees, is equal to

Question 8.

Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to

Question 9.

Question 10.

From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is s. Then the area of the triangle is

Question 1.

The vertices of a triangle are (0,0), (4,0) and (3,9). The area of the circle passing through these three points is

Question 2.

AB is a diameter of a circle of radius 5 cm. Let P and Q be two points on the circle so that the length of PB is 6 cm, and the length of AP is twice that of AQ. Then the length, in cm, of QB is nearest to

Question 3.

In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, is

Question 4.

If the rectangular faces of a brick have their diagonals in the ratio 3:2√3:√153 : 2 \surd3 : \surd{15}3:2√3:√15, then the ratio of the length of the shortest edge of the brick to that of its longest edge is

Question 5.

The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length of each side being 20 cm. The vertical height of the pyramid, in cm, is

Question 6.

Let ABC be a right-angled triangle with hypotenuse BC of length 20 cm. If AP is perpendicular on BC, then the maximum possible length of AP, in cm, is

Question 7.

In a triangle ABC, medians AD and BE are perpendicular to each other, and have lengths 12 cm and 9 cm, respectively. Then, the area of triangle ABC, in sq cm, is

Question 8.

Question 9.

In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm, respectively. Let P be a point on CD such that AP is perpendicular to CD. Then the area, in sq cm, of triangle APD is

Question 10.

A triangle ABC has area 32 sq units and its side BC, of length 8 units, lies on the line x = 4. Then the shortest possible distance between A and the point (0,0) is

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Let $\triangle ABC$ be an isosceles triangle such that AB and AC are of equal length. AD is the altitude from A on BC and BE is the altitude from B on AC. If AD and BE intersect at O such that $\angle AOB = 105^\circ$ , then $\frac{AD}{BE}$ equals

If a triangle ABC, $\angle BCA=50^{0}$ . D and E are points on $AB$ and $AC$ , respectively, such that $AD=DE$ . If F is a point on $BC$ such that $BD=DF$ , then $\angle FDE$ , in degrees, is equal to

If the rectangular faces of a brick have their diagonals in the ratio $3 : 2 \surd3 : \surd{15}$ , then the ratio of the length of the shortest edge of the brick to that of its longest edge is