Math, asked by shankararyal737, 3 months ago

WXYZ is a eyelie quadrilateral. If the bisectors of XXWZ
and XYZ meet the circle at the poinhts A and B
respectively then prove that AB is the diameter of the circle​

Answers

Answered by KishoreKalyanYadav
1

Answer:

Given

that the bisectors of angle W and angle Y of a cyclic quadrilateral WXYZ meet the circle at A and B respectively.

A

and

B

are joined.

RTP

To prove that AB is the diameter of the circle.

Construction

A

and

Y

are joined.

Proof

Sum of opposite angles of a cyclic quadrilateral being

180

we have for cyclic quadrilateral

W

X

Y

Z

X

W

Z

+

X

Y

Z

=

180

1

2

X

W

Z

+

1

2

X

Y

Z

=

1

2

×

180

X

W

A

+

X

Y

B

=

90

[ since WA and YB are bisectors of

X

W

Z

and

X

Y

Z

respectively.]

Bur

X

W

A

=

X

Y

A

, being the angles on same arc

A

X

So We have

X

Y

A

+

X

Y

B

=

90

A

Y

B

=

90

This means

A

B

must be diameter of the circle.

Answered by godgress
2

Answer:

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