|Theorem: If two Circles touch each other internally or externally, the point of contact and the centers of the circles are collinear.|
Data: Two circles with centers A and B touch each other externally at point P (Figure on the left) or internally.
To prove: A, B and P are collinear
Construction: Draw the common tangent RPQ at P. Join AP and BP
For internally touching circles
Theorem: The tangents drawn to a circle from an external point are
To Prove :
Example: In the figure, XY and PC are common tangents to 2 touching circles. Prove that angle XPY = 90o
Theorem: If a chord(AB) and a tangent(PT) intersect externally, then the product of lengths of the segments of the chord (PA.PB) is equal to the square of the length of the tangent(PT2)from the point of contact(T) to the point of intersection (P).
Directions: Solve the following.