Circle Geometry Question (1 Viewer)

[norez]

I was re-doing my Prelim exam from last year, and I still can't do this question. I feel like such a failure haha. I can't see how to do it. So:

O is the centre of the circle. TP is a tangent touching the circle at P. A is a point on the circle such that angle AOT is a right angle. AP cuts OT at Q.



Show that TP= TQ.

 

[xV1P3R]

angle OAQ = angle OPQ (Equal angles are opposite equal sides...)

So we let this be P = angle OAQ = angle OPQ

angle OPT = angle OPQ + angle QPT
90 = P + angle QPT (Angle between tangent and radius...)
angle QPT = 90 - P

Looking at triangle AQO
90 + angle OAQ + angle AQO = 180
P + angle AQO = 90
angle AQO = 90 - P
angle TQP = 90 - P (Vertically opposite..)

therefore TQ = TP (Equal sides opposite...)