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Ex 10.5, 7 - If diagonals of cyclic quadrilateral are diameters - Ex 10.5

Ex 10.5, 7 - Chapter 10 Class 9 Circles - Part 2
Ex 10.5, 7 - Chapter 10 Class 9 Circles - Part 3

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Ex 10.5, 7 If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle. Given: Let ABCD be a cyclic quadrilateral where diagonals AC & BD are diameters, To prove: ABCD is a rectangle Proof: A rectangle is a parallelogram with one angle 90 So, we first prove ABCD is a parallelogram, then one angle 90 Since BD is the diameter Arc BAD is a semicircle, So, BAD = 90 Also, ABCD is a cyclic quadrilateral Sum of Opposite angles of cyclic quadrilateral is 180 So, in quadrilateral ABCD A = B = C = D = 90 Since A = C & B = D , i.e. both pairs of opposite angles are equal ABCD is a parallelogram Also, all angles are 90 So, ABCD is a parallelogram with one angle 90 Therefore, ABCD is a rectangle Hence proved

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Davneet Singh

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.