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Question

In the following figure, ΔABC is an isosceles triangles with perimeter 40 cm. The base AC is of length 10 cm. Side AB and side BC are congruent. A circle touches the three sides as shown in the figure below. Find the length of the tangent segment from point B to the circle.
598682_566081874e9e4eb2b656528274e89bf4.png

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Solution

Let,BP=BR=x.....(i)AP=AQ=y.....(ii)andCQ=CR=z......(iii) (The length of two tangent segments to a circle from an external point are equal.)
AC = 10 cm (Given)
Perimeter of ΔABC=40 cm (Given)
AB+BC+CA=40
(AP+BP)+(BR+CR)+(AQ+CQ)=40
y+x+x+z+y+z=40
2(x+y+z)=40
x+y+z=20
x+(y+z)=20
x+AC=20
x+10=20
x=2010
x=10
BP=BR=10 cm
Length of a tangent segment from point B to the circle is 10 cm.
625433_598682_ans_d6e501fc77a44625a37460bd9809372f.png

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