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Angle in a Semicircle

In triangle A...

Question

In triangle ABC, $A B = 3, B C = 4, A C = 5$ then radius of circle touching all the three sides is

A

4

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B

1

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C

2

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D

3

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Solution

The correct option is B $1$
By Pythagoras Theorem,
⇒ AC² = AB²+ BC²Given in ΔABC, AB = 3, BC = 4, AC = 5.
⇒ 5² = 3² + 4²⇒ 25 = 25
∴ ΔABC is a right angled triangle and ∠B is a right angle.
We know that the radius of the circle touching all the sides is (AB + BC – AC )/ 2
⇒ The required radius of circle = (3 + 4 – 5 )/2 = 2/2 = 1

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