The vertices of a right angled triangle are on a circle of radius R and the sides of the triangle are tangent to inscribed circle of radius r. If the lengths of the sides about the right angles are 16 and 30, then the value of (R + r) equals

Engineering

Mathematics

Basic Rules of Properties of Triangle

Question

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We know that r = $\frac{Δ}{s} = \frac{240}{40} = 6 and R = \frac{34}{2} = 17$

Now Δ = $\frac{1}{2} (16) (30) = 240$

and s = $\frac{16 + 30 + 34}{2}$ =40

Hence (R + r) = 17 + 6 = 23

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