In ABC with usual notation, let and . If r is the inradius and R is the circumradius of ; then is equal to.

JEE MainMathematicsEasy

In $\Delta$ ABC with usual notation, let
$\angle A = 36^{\circ},\angle B = 54^{\circ}\$ and $\angle C = 90^{\circ}$ .
If r is the inradius and R is the circumradius of $\Delta$ ; then
$\left( \frac{a + b}{r + R} \right)$ is equal to.

Show answer and solution

Use r = (s - c)

tan\frac{C}{2}

= s - c

R = \frac{c}{2}

(

\because

right angle triangle)

\frac{a + b}{r + R} = \frac{a + b}{s - c + \frac{c}{2}} = \frac{a + b}{\left( \frac{a + b}{2} \right)} = 2

Source: Grass-G / M-24 Mathematics Paper 31 Dec.docx

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