Hi all,
I was wondering what the quickest way to solve this question would be? I thought that the tangent solution where the tangent being orthogonal to point B making RPS<135 wasn’t the most obvious solution. Any help would be appreciated!
Can you possibly think of any other way or approach/property to get the answer?
No I don’t think I can. Do you have any in mind?
Exactly.
The tangent solution is the most logical solution to this problem.
Let t be the measure of arc QS, as depicted in the image. The total intercepted arc SQR has measure (90 + t)^{\circ}, where you know that 0^{\circ} < t < 180^{\circ}.
By inscribed angle theorem, \angle RPS must be half the measure of the intercepted arc SQR, and so:
45 <\underbrace{ \frac 12 \left(90 + t\right) }_{\angle RPS}< 135
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Very cool. Thank you.