(solved)Question 11 SSC-CGL 2020 March 4 Shift 1

Question 11
SSC-CGL 2020 Mar 4 Shift 1

In a triangle ABC, AB = AC. A circle is drawn from vertex B such that it touches the side AC at D (where D is the mid-point of AC) and it cuts the side AB at E where AE = 2.5cm. Find the length of side AB.

Solution in Detail

Given D is midpoint of AC

$\displaystyle \therefore AD = \frac{AC}{2}$

But also given AC = AB

$\displaystyle \therefore AD = \frac{AB}{2}\text{. . . (1)}$

Observe that AD is a tangent and AEB is a secant. So the tangent secant theorem can be applied:

$\displaystyle AD^2 = AE \times AB$

Using (1), and also that AE = 2.5 cm,

$\displaystyle \bigg(\frac{AB}{2}\bigg)^2 = 2.5 \times AB$

$\displaystyle \implies AB = 10 \text{ cm }\underline{Ans}$