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Ex 10.5, 11 - ABC and ADC are two right triangles with - Cyclic quadrilaterals

Ex 10.5, 11 - Chapter 10 Class 9 Circles - Part 2

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Ex 10.5, 11 ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD. Given: ∆ABC with ∠ B = 90° & ∆ADC with ∠ D = 90° To prove: ∠CAD = ∠CBD Proof: Considering quadrilateral ABCD ∠B + ∠D = 90° + 90° ⇒ ∠B + ∠D = 180° So, sum of one pair of opposite angles of quadrilateral ABCD is 180° ∴ ABCD is a cyclic quadrilateral We draw a circle in which ABCD is a cyclic quadrilateral We consider AC as diameter and draw a circle For points C & D, & segment CDABC ∠CAD & ∠CBD are angles in the same segment So, they must be equal ∴ ∠CAD = ∠CBD Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.