I need help with an extension 1 circle geometry question. (1 Viewer)

[abdullion]

Please help if you can! The questions is:
AB and AC are two chords of a circle on opposite sides of center O. P and Q are the mid-points of AB and AC respectively. Prove that A, P, O and Q are con-cyclic.

 

[swagswagyoloswag]

Construct OP and OQ. Since midpoint of AB is P, then the line OP must be perpendicular to the chord (radii bisecting a chord is at a right angle, or a theorem like that). Therefore, angle APO = 90. This is similar with angle AQO. Since Q is midpoint of AC then OQ is perpendicular. Since angle AQO = 90 and angle APO = 90, angle APO + angle AQO = 90+90= 180. Since opposite angles of a quadrilateral are supplementary then the quadrilateral lies on a circle and is therefore concyclic.

 

[abdullion]

I seeeeeee, thank you so much! Haha, seems so simple once you have it explained. Thanks c: