dout on circle

Tangents drawn from the point P(3,8) to the circle x^2+y^2-6x-4y-11=0 touches the circle

at the point A and B . Then equation of circumcircle of a Triangle PAB is

I have a doubt::

why PO act as a diameter for Circumcenter of a Triangle PAB.

and other question is why circumcircle of PAB is passes through O(3,2)

Thanks

3 Answers

1
rishabh ·

note that angle OBP = angle OAP = 90°
=> PAOB is cyclic quadrilateral.
i hope this clears your doubt.

1
rishabh ·

another thing is that angle in a semicircle = 90°
=> as angle OAP = 90° .:. op is the diameter.

1708
man111 singh ·

Thanks Rishab

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