Parama drew to circles intersect each other at the points P and Q . If the diameter of the two ircels are PA and PB resepctively , then prove that A,Q,B are collinear.

Explanation

Let two circles with centres O and O' intersects each other at P and Q.
PA is a diameter of the circle with centres at O and PB is alos a diameter of the circle at O,
To prove A,Q and B are collinear.
Construction : Let us join P,Q
Proof : In the with centre at `O, angle AQP` is a semi-circular angle `:.anglePQA=1` right angle.
Again, in the circle with centre at `O, angle BQP` is a semicircular angle
Now, `angle PQO+ anglePQB=1` right angle +1 right angle.
or, `angle AQB=2 ` right angle or, `angle AQB=180^(@) or, angle AQB=` straight angle.
`:. angle AQB`=1 straight angle.
Hence the point A,Q,B are colliear.