Question

ABCD is such a quadrilateral that A is centre of circle passing through B , C and D . Prove that " angle CBD+ angle CDB = 1/2 angle BAD . "​

Answer 1

Answer:

Given:- In a circle ABCD is a quadrilateral having center A

To Prove:- angle CBD + angle CDB = 1/2 angle BAD

Construction:- Join AC and BD

Proof:- Since arc DC subtends angle DAC at center and angle CBD at a point B in the remaining part of the circle.

   Thus, angle DAC = 2 angle CBD                                                   ....(i)

In a circle, the angle subtended by an arc at the center is twice the angle subtended by it at the remaining part of the circle.

Similarly, arc BC subtends angle CAB at center and angle CDB at a point D in the remaining part of the circle.

    Thus, angle CAB = 2 angle CDB                                                   ....(ii)

In a circle, the angle subtended by an arc at the center is twice the angle subtended by it at the remaining part of the circle.

On adding equations (i) and (ii),

angle DAC + angle CAB= 2 angle CBD + 2 angle CDB

angle BAD = 2(angle CBD + angle CDB)

angle CBD + angle CBD = 1/2 angle BAD

Hence Proved

Answer 2

Answer:

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