Prelim Circle Geo (1 Viewer)

[khorne]

Hey

The question is attached, along with the diagram.

I've tried a few things, but nothing seems to work...Could someone suggest something, and I'll give it a go.

 

[Trebla]

Connect points A to O and B to O to form OA and OB.
Let angle APB = x degrees
Angle AOB = 2x (angle at centre twice angle at circumference standing on same arc)
But OBQA is a cyclic quadrilateral, hence
Angle BQC = 180 - 2x (opposite angles supplementary in cyclic quadrilateral)
Consider angle sum of triangle PQA
x + 180 - 2x + angle PAQ = 180
=> angle PAQ = x
This means angle QPA = angle QAP, hence triangle PQA is isosceles, thus
PQ = QA (equal opposite sides of equal opposite angles)

 

[khorne]

Ahh, Thank's a lot...I feel really stupid now, missing the fact that OBQA is a cyclic quad...