Geometry Question (1 Viewer)

[Dreamerish*~]

PQRS is a cyclic quadrilateral and A is any point on PQ. A circle through the points P, A and R cuts RS produced at B.

Prove that BA || SQ

Graph attached.

 

[shafqat]

Use angles standing on the same arc:
<ABR = <RPA = <QSR.
So \\ lines because of corresponding angles.

 

[insert-username]

Let angle SQP be x.

Angle SRP = x (equal angles stand on equal chords)

Angle SRP also stands on chord BP.

Therefore Angle BAP = x (equal angles stand on equal chords)

Therefore Angle BAP = Angle SQP.

But Angle BAP corresponds to Angle SQP.

Therefore SQ // BA (corresponding angles in parallel lines are equal)


That should do it.


I_F

 

[Dreamerish*~]

Oh how simple it sounds now.

Thank you.

 

[insert-username]

No problemo.


I_F