JEE MainMathematicsTough

In a $\Delta$ ABC, b = 12 units, c = 5 units and $\Delta$ = 30
square units. If d is the distance between vertex A and incenter of the
triangle then the value of d^4 is

Show answer and solution

Al = rcosec\frac{A}{2} = \frac{\Delta}{S}cosec\frac{A}{2}

\Delta = \frac{1}{2}bc\ sinA

sinA = 1

\Rightarrow A = \frac{\pi}{2}

a^2 = b^2 + c^2

\Rightarrow

a = 13
Al = 2

\sqrt{2}

units

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

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