Common tagents to two circles | Common Chord | Chord with given mid point

PP' and QQ' are two direct common tangents at two circles intersecing in point A and B .The common chord produced intersects PP' in R and QQ' in S.prove that RS^(2)=PP^(2)+AB^(2)

The locus of the centers of the circles such that the point (2,3) is the mid point of the chord 5x+2y=16 is

The locus of the centers of the circles such that the point (2,3) is the mid point of the chord 5x+2y-=16

Prove that tangent drawn at the mid point of the are of a circle is pallelar to the chord joing the ends of point of the are

Question on common tangent || Equation OF common chord ||length OF common chord

Chord Of Contact|Pair Of Tangents|Director Circle|Equation Of Chord With Mid Point|Properties Of Ellipse|OMR

From a pt A common tangents are drawn to a circle x^(2)+y^(2)=(a^(2))/(2) and y^(2)=4ax. Find the area of the quadrilateral formed by common tangents,chord of contact of circle and chord of contact of parabola.

Two circles with centres O and O' of radii 3 cm and 4 cm , respectively intersect at two points P and Q such that OP and O'P are tangents to the two circle . Find the length of the common chord PQ.