As shown in the adjoining figure , two circles centred
at A and B are touching at C. Line passing through C
intersects the two circles at M and N respectively.
Show that seg AM `||`seg BN.

In the adjoining figure,the circles with centres P and Q touch eahc other at R.A line passing through R meets the circles A and B respectively then,Prove that (i) Seg AP||seg BQ

In the adjoining figure ,two circles intersect at points M and N. | Secants drawn through M and N intersect the circles at points R,S and P,Q respectively. Prove that: seg SQ || seg RP.

In the adjoining figure.circles with centres X,Y touch each other at Z.A secant passing through Z meets the circles at A and B respectively.Prove that, radius XA||radius YB .Fill in the blanks and complete the proof.

In the adjoining figure, circles with centres X and Y touch internally at point Z. Seg BZ is a chord of bigger circle and it intersects smallest circle at point A. prove that, seg AX || seg BY.

In the adjoining figure,the circles with centre A and B touch each other at E Line l is a common tangent that touches the circle at C and D respectively.Find length of seg CD if the radii of the circles are 4 cm,6 cm?

In the adjoining figure, two circles with centres O and P are touching internally at point A. If BQ = 9. DE = 5, then find the radii of the circles.

In the adjoining figure, two circles intersect each other at points A and E. Their common secant through E intersects the circle at points B and D. The tangents of the circles at point B and D intersect each other at point C. Prove that square ABCD is cyclic.

In the adjoining figure, two circles intersect each other at point M and N. Secants drawn from point M and N intersect cirlces at point R, S, P and Q as shown in the figure. Prove that seg PR || seg QS

As shown in the adjoining figure, two chords AB and CD of the same circle are parallel to each other. P is the centre of the circle. Show that angleCPA = angleDPB .

In the adjoining figure, two circles intersect each other in point R and point S. Line PQ is a common tangent touching circle at points P and Q. Prove that /_PRQ+/_PSQ=180^@