0

Guest

Courses New

WXYZ is a cyclic quadrilateral.if the bisectors of angle XWZ and 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 the bisectors of angle XWZ and 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

Aditya Gupta
2081 Points
2 years 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.
kindly approve :)
Vikas TU
14149 Points
2 years ago
Dear student 
Sum of opposite angles of a cyclic quadrilateral being 
180
∘
 we have for cyclic quadrilateral
Angle XWZ + Angle XYZ = 180 
XWA + XYB = 90 
XWA = XYA being the angles on same arc AX 
So XYA + XYB = 90 
AYA = 90 
This means AB must be diameter of the circle. 
Good Luck 

Think You Can Provide A Better Answer ?

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

Other Related Questions on 10 grade maths

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More