In the given figure, two circles with centres O and O' touch externally at a point A. A line through A is drawn to intersect these circles at B and C. Prove that the tangents at B and C are parallel.

In the given figure, two circles touch each other externally at the point C. Prove that the common tangent to the circle at C bisects the common tangents at P and Q.

In the given figure, two equal circles with centres O and O' touch each other at X. OO' produced meets the circle with centre O' at A. AC is a tangent to the circle with centre O at the point C. O'D is perependicular to AC. Find the value of (DO')/(CO) .

In the given figure, AD is a diameter of a circle with centre O and AB is a tangent at A. C is a point on the circle such that DC produced intersects the tangent at B and |__ABD=50^(@) . Find |__COA .

Let A be one point of intersection of two intersecting circles with centres O and Qd . The tangents at A to the two circles meet the circles again at B and C respectively. Let the point P be located so that AOPQ is a parallelogram. Prove that P is the circumcentre of the triangle ABC.

Locus of the centre of a circle which touches given circle externally is :

Prove that the tangents to a circle at the end points of a diameter are parallel.

In the given figure ,XY and XY are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X'Y' ar B.Prove that angleAOB=90^(@)

In the given figure PQ & RS are two parallel tangents to a circle o and another tangent AB with point of contact C intersecting PQ at A and RS at B. Prove that angleAOB = 90^@

Two circle intersect at two points B and C. Through B, Two lines segment ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively. Prove that ACP = QCD .

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