In figure 3.99, seg MN is a chord of a circle with centre O. MN = 25,L is a point on chord MN such that ML = 9 and d(O,L) = 5.

Find the radius of the circle.

In figure 3.97, circles with centres C and D touch internally at point E. D lies on the inner circle. Chord EB of the outer circle intersects inner circle at point A. Prove that, seg EA ≅seg AB.

In figure 3.98, seg AB is a diameter of a circle with centre O . The bisector of∠ ACB intersects the circle at point D. Prove that, seg AD ≅seg BD.

Complete the following proof by filling in the blanks.

Proof: Draw seg OD.

…90° ............ angle inscribed in semicircle

........45° .... CD is the bisector of

m(arc DB) = ........45° .. inscribed angle theorem

…............90° definition of measure of an arc (I)

seg OA ≅seg OB .......radii of the circle... (II)

∴line OD is of seg AB ......bisector.... From (I) and (II)

∴seg AD ≅seg BD

In figure 3.100, two circles intersect each other at points S and R. Their common tangent PQ touches the circle at points P, Q.

Prove that, ∠ PRQ + ∠ PSQ = 180°

In figure 3.101, 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.