This question is similar to Chapter 10 Class 10 Circles - Ex 10.2

Please check the question here

https://www.teachoo.com/1838/539/Ex-10.2--12---A-triangle-ABC-is-drawn-to-circumscribe-a-circle/category/Ex-10.2/

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Question 33 – Part 2 Prove that the lengths of tangents drawn from an external point to a circle are equal. Using above result, find the length BC of 𝛥ABC. Given that, a circle is inscribed in 𝛥ABC touching the sides AB, BC and CA at R, P and Q respectively and AB= 10 cm, AQ= 7cm ,CQ= 5cm. From theorem 10.2, Lengths of tangents drawn from external point are equal Hence, AR = AQ = 7 cm CP = CQ = 5 cm BP = BR Since AB = 10 cm, and AR = 7 cm, ∴ BR = 3 cm Thus, BP = BR = 3 cm Now, BC = BP + CP = 3 + 5 = 8 cm

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.