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` .

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 given figure, two circles touch each other externally at point P. AB is the direct common tangent of these circles. Prove that: (i) tangent at point P bisects AB (ii) angle APB=90^(@)

Two circles touch each other internally. Show that the tangents drawn to the two circles from any point on the common tangent, are equal in length.

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.

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 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 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

Two circles with centres A and B intersect each other at points P and Q. Prove that the centre-line AB bisects the common chord PQ perpendicularly.

In the given figure, there are two circles with centers A and B. The common tangent to the circles touches them, respectively,at P and Q. AR is 40cm and AB is divided by the point of contact of the circles in the ratio 5:3 The radius of the circle with center B is

In Figure, two equal circles touch each other at T , if Q P=4. 5 c m , then Q R= (a) 9cm (b) 18cm (c) 15cm (d) 13.5cm