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Circles with radii 3, 4 and 5 touch each other externally if P is th.pdf

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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 Solution Let A, B, C be the centre of the three circles. Clearly the point P is the in–centre of the ?ABC, and hence r = s (s a)(s b)(s c) (s a)(s b)(s c) s s s ? - - - - - - = = Now 2s = 7 + 8 + 9 = 24 ? s = 12. Hence r = 5. 4.3 5 12 = ..

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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 Solution Let A, B, C be the centre of the three circles. Clearly the point P is the in–centre of the ?ABC, and hence r = s (s a)(s b)(s c) (s a)(s b)(s c) s s s ? - - - - - - = = Now 2s = 7 + 8 + 9 = 24 ? s = 12. Hence r = 5. 4.3 5 12 = .

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  • 1. 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 Solution Let A, B, C be the centre of the three circles. Clearly the point P is the in–centre of the ?ABC, and hence r = s (s a)(s b)(s c) (s a)(s b)(s c) s s s ? - - - - - - = = Now 2s = 7 + 8 + 9 = 24 ? s = 12. Hence r = 5. 4.3 5 12 = .