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Standard X

Mathematics

Tangents from External Points

In the given ...

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.

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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 cm

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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.

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 cm

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.