Question

Ch- circles Ex -circle through three points
Q-ABC and ADC are row right triangles with common hypotenuse ACproce that angle CAD = angle CBD.
Q-prove that a cyclic parallelogram is a rectangle.

Answer 1

Draw rough figure.
Ans of Q.1)by isosceles triangle theoram.....and by alterbate angles theorem
Ans of Q.2)Cyclic quadrilateral have its adjacent ngles SUPPLEMENTARY.

Answer 2

Hello mate ☺

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Solution:

AC is the common hypotenuse for two right triangles, ∆ABC and ∆ADC.

∠ABC=∠ADC=90°        (Given)

⇒∠ABC+∠ADC=180°

(If sum of a pair of opposite angles of a quadrilateral is 180°, the quadrilateral is cyclic.)

Therefore, quadrilateral ABCD is cyclic.

⇒∠CAD=∠CBD.    (Angles in the same segment are equal)

I hope, this will help you.☺

Thank you______❤

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