First slide

Properties of triangles

Question

The area of the right angled triangle interms of its circumradius and inradius is

Moderate

A

$r (r + 2 R)$
B

$r (2 r + R)$
C

$R (r + 2 R)$
D

$R (R + r)$

Solution

$\begin{array}{l} Δ = r . s \\ = r (s - a + a) \\ = r \{(s - a) \tan \frac{A}{2} + 2 R \sin A\} (∵ A = 90) \\ = r (r + 2 R) \end{array}$

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