Two circles touch externally at a point P. From a point T on the tangent at P, tangents TQ and TR are drawn to the circles with points of contact Q and R respectively. Prove that TQ = TR

Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that /_ PTQ = 2 /_ OPQ .

Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that angle PTQ=2angleOPQ .

Fill in blanks- From a point outside a circle exactly ___tangents can be drawn to the circle.

Fill in blanks- The tangent at any point of a circle is ______to the radius through the point of contact.

The circle C1 : x^2 + y^2 = 3 , with center at O, intersects the parabola x^2 = 2y at the point P in the first quadrant. Let the tangent to the circle C1 at P touches other two circles C2 and C3 at R2 and R3, respectively. Suppose C2 and C3 have equal radii 2sqrt(3) and centers Q2 and Q3, respectively.If Q_2 and Q_3 lies on the y-axis, then

Three circles touch one another externally. The tangents at their points of contact meet at a point whose distance from a point of contact is 4. Find the ratio of the product of the radii to the sum of the radii of the circles.

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

TP and TQ are any two tangents to a parabola and the tangent at a third point R cuts them in P' and Q' . Prove that (TP')/(TP)+(TQ')/(TQ)=1

Fill in the blank : A tangent to a circle intersects it in_______point (s).