Two circles intersect each other at point A and B. Their common tangent touches the circles at points P and Q as shown in the figure. Show that the angles PAQ and PBQ are supplementary.

Two circles intersect each other at points A and B. A straight line PAQ cuts the circles at P and Q. If the tangents at P and Q intersect at point T, show that the points P, B, Q and T are concylic.

Two circles touch each other internally at point P. QPR is the tangent at P, segments PAB and PCD meet circles at points, A,B,C and D as shown in the figure. Show that chord AC is parallel to chord BD.

Two congruent circles intersect each other at points A and B. Through A any linesegment PAQ is drawn so that P, Q lie on the two circles. Prove that B P\ =\ B Q .

In Figure, two circles touch each other at the point C . Prove that the common tangent to the circles at C , bisects the common tangent at P and Q .

Two circles touch each other externally at point P. Q is a point on the common tangent through P. Prove that the tangents QA and QB are equal.

In the figure, two circles touch each other at the point C.Prove that the common tangents to the circles at C, bisect the common tangents at P and Q.

In the figure, two circles intersect each other at points A and B. AP and AQ are the diameters of these circels. Prove that PBQ is a straight line.

In the figure, two circles intersect each other at points A and B. AP and AQ are the diameters of these circels. Prove that PBQ is a straight line.

Let P and Q be 2 circles externally touhing each other at point X. Line segment AB is a direct common tangent to circle P and Q at points A and B respectively. Another common tangent to P and Q at X intersects line AB at a point Y. If BY = 10 units and the radius of P is 9 units, then the value of the reciprocal of the radius of the radius of the circle Q is equal to

Two equal circles touch each other externally at C and A B is a common tangent to the circles. Then, /_A C B= 60o (b) 45o (c) 30o (d) 90o