Geometry Problem#1

Geometry Level 3

The lengths of the sides containing the right angle in a right angled triangle are 3 3 and 4 4 units respectively. Find the distance from the vertex of the right angle to the nearest point on the inscribed circle.

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The answer is 0.415.

Anik Mandal by Anik Mandal , 21, India

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1 solution

Aaaaa Bbbbb
Dec 24, 2014

According to Heron formula: r × ( 3 + 4 + 5 ) 2 = 3 × 4 2 = 6 ⇒ r = 1 r \times \frac{(3+4+5)}{2} = \frac{3 \times 4}{2}=6 \Rightarrow r=1 D m i n = 2 − 1 = 0.415 D_{min}=\sqrt{2}-1=\boxed{0.415}

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