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  • Three circles of radii 3, 4 and 5 units touches each other externally and the tangents drawn at the point of contact A intersect at P. Find distance between point P and point of contact A

Three circles of radii 3, 4 and 5 units touches each other externally and the tangents drawn at the point of contact A intersect at P. Find distance between point P and point of contact A.

Option: 1

\sqrt{6}


Option: 2

\sqrt{10}


Option: 3

\sqrt{5}


Option: 4

5


Answers (1)

best_answer

\mathrm{\text { Obviously, } P A \text { is inradius of triangle } C_1 C_2 C_3 \text {. }}

\mathrm{\text { So, } r=\frac{\Delta}{s}=\frac{\sqrt{s(s-a)(s-b)(s-c)}}{s}}

Sides of triangle are 7, 8, 9

\mathrm{\text { and } s=\frac{7+8+9}{2}=12}

\mathrm{\text { So, } r=\frac{\sqrt{12 \cdot 5 \cdot 4 \cdot 3}}{12}=\sqrt{5}}

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