Question

In the adjoining figure, triangle ABC is an isosceles triangle with perimeter 44cm. The base BC is of length 12 cm. Sides AB and AC are congruent. A circle touches the three sides as shown. Find the length of a tangent segment from A to the circle.​

Answer 1

The length of the tangent is 10 cm

Perimeter of the Triangle = 44cm  (Given)

Base of the Triangle = 12cm  (Given)

In ΔABC

AP = AQ, BP = BR and CR =  CQ  ( As tangents from an external point are equal)

Now, AB + AC + BC = 44 cm,

Therefore,

AP + BP + AQ + CQ + BC = 44

AP + BR + AQ + CR + BC = 44

AP + AQ + BR + CR + BC = 44

AP + AQ + BC  + BC = 44

2AP + 2BC = 44

2AP = 44 −-24

2AP = 20 cm

AP = 10

Answer 2

Step-by-step explanation:

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