Question

A circle is inscribed in a right-angled triangle, right angle at C. If AC = 18 cm, BC = 24 cm,
then find the length of the radius of the circle.​

Answer 1

Answer:

8cm will be the radius

of the circle

Answer 2

Answer: 6cm

Step-by-step explanation:

We know that the radius of the incircle of a triangle is equal to

• The Area of the Triangle/ The Semiperimeter of the Triangle

So for the ∆ABC, the radius is given by • ar(∆ABC)/(AB+BC+AC)/2

Since ∆ABC is right angled at C, by the Pythagoras Theorem we can get

• (AB)² = (AC)² + (BC)²

• AB = √(AC)²+ (BC)²

• AB = √18²+24²

• AB = √900 = 30cm

The Semiperimeter = AB+BC+AC/2

= 24+18+30/2

= 72/2 = 36cm ------(i)

The area of ∆ABC = 1/2 x BC x AC

= 1/2 x 24 x 18

= 12 x 18 = 216cm² -------(ii)

On dividing (ii) by (i) - 216/36 = 6cm

Thus, 6cm is the radius of the inscribed circle.