CAT 2025 Lesson : Class Discussion: Geometry - Lines & Triangles: 17 to 24

Class Discussion – Lines and Triangles

Question 17

Let AB, CD, EF, GH and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K and O so as to form a triangle?

Answer: 160

Question 18

Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB. If the perpendicular distance of P from each of AB, BC and CA is

4(\sqrt{2} - 1)

cm, then the area, in sq cm, of the triangle ABC is

Answer: 16

Question 19

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
[CAT 2018 S1]

		$192\sqrt{3}$
		$164\sqrt{3}$
		$188\sqrt{3}$
		$248\sqrt{3}$

Question 20

Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which one of the following pairs can represent, in cm, the possible length and breadth of ABCD?
[CAT 2018 S1]

		24, 12
		25, 10
		24, 10
		25, 9

Question 21

On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, is
[CAT 2018 S2]

Answer: 24

Question 22

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
[CAT 2019 S2]

		$8\sqrt{2}$
		10
		5
		$6\sqrt{2}$

Question 23

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
[CAT 2019 S2]

		72
		68
		80
		78

Question 24

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
[CAT 2020 S2]

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

Want to read the full content

Unlock this content & enjoy all the features of the platform

Subscribe Now