Sum

ABC is a right-angled triangle, right-angled at A. A circle is inscribed in it. The lengths of the two sides containing the right angle are 5 cm and 12 cm. Find the radius of the circle

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#### Solution

Given that ∆ABC is right angled at A.

AC = 5 cm and AB = 12 cm

BC^{2} = AC^{2} + AB^{2} = 25 + 144 = 169

BC = 13 cm

Join OA, OB, OC

Let the radius of the inscribed circle be r

Area of ∆ABC = Area of ∆OAB + Area of ∆OBC + Area of ∆OCA

⇒ 1/2 × AB × AC

`=\frac{1}{2}(12\times r )\text{}+\frac{1}{2}(13\times r )\text{}+\frac{1}{2}(5\times r )`

⇒ 12 × 5 = r × {12 + 13 + 5}

⇒ 60 = r × 30 ⇒ r = 2 cm

Concept: Right-angled Triangles and Pythagoras Property

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