WXYZ is a cyclic quadrilateral.if the bisectors o

Question

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.

Aditya Gupta · Accepted Answer

dear student, first draw the diagram according to the question.now, let angle ZWP= angle PWX= θalso, angle ZYQ= angle XYQ= pcyclic implies ZWX + XYZ = 1802θ + 2p= 180or θ + p= 90now, join PY. and note than ZWP= PYZ= θ (angles in the same segment theorem)so, PYQ= PYZ + ZYQ= θ + p= 90or 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 :)

10 grade maths> WXYZ is a cyclic quadrilateral.if the bis...

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.

Umangsingsarumagar , 5 Years ago

Aditya Gupta

Vikas TU

LIVE ONLINE CLASSES

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10 grade maths> WXYZ is a cyclic quadrilateral.if the bis...

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.

Umangsingsarumagar , 5 Years ago

Aditya Gupta

Vikas TU

LIVE ONLINE CLASSES

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