Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

WXYZ is a cyclic quadrilateral.if bisectors of angle XWZ and angle angle XYZ meet the circle at the points P and Q respectively, then prove that PQ is the diameter of the circle.

WXYZ is a cyclic quadrilateral.if bisectors of angle XWZ and angle angle XYZ meet the circle at the points P and Q respectively, then prove that PQ is the diameter of the circle.

Grade:10

2 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
one year ago
576-2172_IMG_20200229_232306.jpg
Vikas TU
14149 Points
one year ago
Dear student 
 
 first draw the diagram according to the question.
now, let angle ZWP= angle PWX= θ
also, angle ZYQ= angle XYQ= p
cyclic implies ZWX + XYZ = 180
2θ + 2p= 180
or θ + p= 90
now, join PY. and note than ZWP= PYZ= θ (angles in the same segment theorem)
so, PYQ= PYZ + ZYQ
= θ + p= 90
or PYQ= 90.
hence PQ is a diameter, since when P and Q are joined to O (centre of circle), angle POQ= 2*pyq= 180. hence, POQ is a straight line, thereby implying that it is the diameter.

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free