**Help Required**: Given a point P in the interior of a circle of radius 1 unit with two perpendicular chords through P and another pair of perpendicular chords through P that make an angle of θ radians with the first pair, as shown in the figure, find the area of the shaded region.

## Comments

Sort by:

TopNewestHint:As suggested by the problem, the answer is independent of the point (as long as it's contained within).Now, figure out how to prove this fact.

In particular, what can we say about how the circumference is split into these regions? – Calvin Lin Staff · 1 year, 3 months ago

Log in to reply

– Lakshya Sinha · 1 year, 2 months ago

I don't understand can you help me?Log in to reply

– One Top · 1 year, 2 months ago

We can consider specific cases and conclude that the answer is 2θ but so far I have not been able to prove it for any general point within the circle. Would 2θ be correct?Log in to reply

– Calvin Lin Staff · 1 year, 2 months ago

Yes, that conjecture is correct.Log in to reply