Circles C(O, r) and C(O', r'), `(r gt r') ` touch internally at P. PQ is a chord of circle C(O, r) which intersects C(O', r') at R. Show that OO'RQ is a trapezium

In Figure,circle C(O,r) andC (O'(r)/(2)) touch internally at a point.Aand AB is a chord of the circle C(O,r) intersecting C(O',(r)/(2)) at C. Prove that AC=CB

Circles C(o, r) and C(O^(1), (r)/(2)) touch internally at a point A and AB is a chord of the circle intersecting C(O^(1), (r)/(2)) at C. Then AC is equal to :

Two circles C(O, r) and C'(O', r') touch externally at P(3, 1). If the co-ordinates of O and O' are (1, p) and (q, -2) repectively. Their areas are in the ratio 4 : 9. Find the value of p^(2)+q^(2) .

Two equal chords AB and CD of a circle C(O,r) when produced meet at a point E. Prove that: BE = DE

Two circles C(0,r) and C(O',r') touch extemally.Show that the length of a common tangent (not through the point of contact of the circles ) is 2sqrt(rr)'

) and In this figure two bigger circles C(0,r) and C(O',r') touch each other.On third circle C(0,r) are touching the two bigger circles as well as the common tangent.Then prove

P Q and R S are two parallel chords of a circle and lines R P and S Q intersect each other at O as shown in Figure. Prove that O P=O Qdot

Diagonals A C and B D of a quadrilateral A B C D intersect at O in such a way that a r(triangle A O D)=a r(triangle B O C) . Prove that A B C D is a trapezium.

If O is the centre of a circle with radius r and AB is a chord of the circle at a distance (r)/(2) from O, then /_BAO=