Question

In a right ∆ABC, the incircle touches the hypotenuse AC at D. If AD = 10 and DC = 3, the inradius of ABC is

(a) 5

(b) 4

(c) 3

(d) 2

Answer 1

Answer is : (d) 2

We have,

ABC is a right angled triangle. AC is hypotenuse of ∆ABC. The incircle touch the hypotenuse at D.

[AD and AF are tangents on a circle from external points are equal]

Similarly, CD = CE = 3

⇒ r = 2, r ≠ -15