Question

# In the given figure $△$ABC is an isosceles triangle with perimeter 44 cm. The base BC is of the 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.

Solution

## AP = AQ, BP = BR and CR =  CQ              (Tangents from a external point are equal) Now, AB + AC + BC = 44 cm                    (Perimeter of triangle ABC) ⇒ 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 ∴ AP = 10 cmMathematicsMathematics (Geometry)Standard X

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