In the figure, quadrilateral ABCD is circumscribing a circle with centre O and AD⊥AB. If radius of incircle is 10cm, then the value of x is

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  1. Class 10
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Transcript

Question 26 In the figure, quadrilateral ABCD is circumscribing a circle with centre O and AD⊥ AB. If radius of incircle is 10 cm, then the value of x is Since Tangent is perpendicular to Radius OS ⊥ AD and OP ⊥ AB Thus, ∠ OSA = 90° and ∠ OPA = 90° And, ∠ SOP = 90° Also, AS = AP (Tangents drawn from external point are equal) Thus, In OPAS, All angles are 90° and Adjacent sides are equal ∴ OPAS is a square So, AP = OS = 10 cm Also, Tangent drawn from external point are equal ∴ CQ = CR = 27 cm And, BP = BQ Given CB = 38 cm CQ + BQ = 38 CQ + BP = 38 27 + BP = 38 BP = 38 − 27 BP = 11 cm Thus, x = AB = AP + BP = 10 + 11 = 21 cm

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.