Three Circles With Radii 3 Cm, 4 Cm And 5 Cm Touch Each Other Externally. If A Is The Point Of Intersection Of Tangents To These Circles At Their Points Of Contact, Then The Distance Of A From The Points Of Contact Is

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Question

Three circles with radii 3 cm, 4 cm and 5 cm touch each other externally. If A is the point of intersection of tangents to these circles at their points of contact, then the distance of A from the points of contact is

Solution

Correct option is

From the fig it is clear that A is the centre of the in-circle of the trianglePQR formed by the lines joining the centres of the given circles. We have PQ = 5 + 4 = 9, QR = 4 + 3 = 7, RP = 3 + 5 = 8, distance of from the points of contact is the radius r of the in-circle of triangle PQR. From trigonometry r = Δ/s where Δ is the area and 2s is the perimeter of the triangle PQR

   

                                                                                   

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