Find the radius

Geometry Level 2

The figure above shows a circle inscribed in a quarter circle with radius 10 10 . Find the radius of the circle correct to three decimal places.


The answer is 4.142.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

By the pythagoreran theorem, O P = r 2 + r 2 = r 2 OP=\sqrt{r^2+r^2}=r\sqrt{2}

O T = r + O P = r + r 2 OT=r+OP=r+r\sqrt{2} ⟹ \implies 10 = r ( 1 + 2 ) 10=r(1+\sqrt{2}) ⟹ \implies r = 4.142 \color{#D61F06}\boxed{r=4.142}

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