class 9 circles

1) Draw using compasses only two circles that are orthogonal (That intersect
at right angles. Ie; such that the tangents to the circles at a point of their
intersection are perpendicular.
2) Two intersecting circles C1 and C2 have common tangents which touches C1
at P and C2 at Q. The two circles meet at M and N where N is nearer to PQ
than M is. The line PN meets the circle C2 again at R. Prove that MQ bisects
angle PMR ?
3) ABCD is a quadrilateral inscribed in a circle. Diagonal BD divides AC into two
segments, one of which is twice as long as other. If AB =10, AD = 12 and DC
= 11 Find BC?
4) Triangle ABC is right angled at A and the radius AB cuts BC and AC internally
at points D and E respectively. If BD = 20 and DC = 16 Find AC