NCERT Solutions for Class 9 Maths Chapter 10

Important NCERT Questions

Circles

NCERT Books for Session 2022-2023

CBSE Board, UP Board and Other state Boards

EXERCISE 10.5

Page No:185

Questions No:7

# If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

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AC is Diameter of circle.

Hence, ∠ADC = 90° and ∠ABC = 90° …(1) [∵ Angle in a Semicircle is a right angle.]

Similarly, BD is Diameter of circle.

Hence, ∠BAD = 90° and ∠BCD = 90 …(2) [∵ Angle in a semicircle is a right angle.]

From the equation (1) and (2), ∠ADC = ∠ABC = ∠BAD = ∠BCD = 90°

Hence, ABCD is a rectangle.