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Circles with radii 3, 4 and 5 touch each other externally if P is the point of intersection of tangents to these circles at their points of contact. Find the distance of P from the points of contact.

Circles with radii 3, 4 and 5 touch each other externally if P is the point of intersection of tangents to these circles at their points of contact. Find the distance of P from the points of contact.

Grade:10

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
6 years ago
Hello Student,

Let A, B, C be the centre of the three circles.
=>P is the in–centre of the ∆ABC
\\=>r=\Delta/s=\sqrt{(s-a)(s-b)(s-c) \over s} \\=>2s=7+8+9=24 \\=>s=12 \\r=\sqrt5

Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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