Question

in a right triangle ABC, right angle d at B, BC=5cm and AB=12cm . A circle is touching the side of triangle ABC. Find the radius of the circle​

Answer 1

Answer:

QUESTION :-

In a right triangle ABC, right angle d at B, BC=5cm and AB=12cm . A circle is touching the side of triangle ABC. Find the radius of the circle.

SOLUTION :-

In right triangle ABC ,

By using pythagoras theorem , we have

AC² = AB² + BC²

= 5² + 12²

= 25 + 144

= 169

☆AC² = 169

=> AC = 13 cm

Now,

ar(ABC) = ar(AOB) + ar(BOC) + ar(AOC)

1/2 × AB × BC = 1/2 × OP × AB + 1/2 × OQ × BC + 1/2 × OR × AC

5 × 12 = x × 5 + x × 12 + x × 13

60 = 30x

60/30 = x

2 = x

[ RADIUS OF CIRCLE :- 2 cm ]