A circle touches the side BC of triangle ABC at D & AB and AC is produced to E and F respectively to touch the circle. If AB = 10 cm, AC = 8.6 cm & BC = 6.4 cm then BE = ?
Show answer & explanation
Correct answer: D
Explanation
Note: The question has been modified since it was incorrect according to the answer key released by the SSC.
The correct answer is option 4 i.e 2.5 cm.
Given: AB = 10 cm, BC = 6.4 cm, AC = 8.6 cm
As the circle touches side BC at D, let BD = x, DC = y
BD + DC = 6.4 (Given in the question)
⇒ x + y = 6.4 --------------- eqn (1)
Then,
BE = x, CF = y (Lengths of tangents from the same point outside the circle are equal)
As AE touches the circle at point E and AF touches the circle at point F only:
AE = AF
⇒ AB + BE = AC + CE
⇒ 10 + x = 8.6 + y
⇒ y - x = 1.4 -------------- eqn (2)
From eqn 1 and eqn 2, we get,
x = 2.5 cm = BE