Question

The bisectors of P and R of a cyclic quadrilateral PQRS meet at X. PX produced meets at the circle at Y. prove that angle(XRY)= 90.

Answer 1

Answer:

R.E.F image

Give; The Bisectors of angle w and angles y of a circle quadrilateral

wxyz meet the circle at A and B resp.

A and B are joined.

RTP : To prove that AB is two diameter of the circle

Constructions

A and Y are Joined

Proof :

Sum of opposite angle of a cyclic quadrilateral being 180

∘

we have for cyclic quadrilateral wxyz

∠XWZ+∠XYZ=180

∘

⇒

2

1

∠XWZ+

2

1

∠XYZ=

2

1

×180

∘

⇒∠XWA+∠XYB=90

∘

(since WA and YB are bisectors

of ∠XWZ and ∠XYZ resp.)

But ∠XWA=∠XYB, being the angles on same are AX

So we have,

∠XYA+∠XYB=90

∘

⇒∠XYA+∠XYB=90

∘

⇒∠AYB=90

∘

____(1)

Eq.

n

(1) must be shows that AB is Two diameter of the circle.

Step-by-step explanation:

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Answer 2

Answer:

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