In figure 3.96 P is the point of contact.

(1) If m(arc PR) = 140°,∠ POR = 36°,find m(arc PQ)

(2) If OP = 7.2, OQ = 3.2,find OR and QR

(3) If OP = 7.2, OR = 16.2,find QR.

In figure 3.94,

(1) m(arc CE) = 54°,

m(arc BD) = 23°, find measure of ∠CAE.

(2) If AB = 4.2, BC = 5.4,

AE = 12.0, find AD

(3) If AB = 3.6, AC = 9.0,

AD = 5.4, find AE

In figure 3.95, chord EF || chord GH. Prove that, chord EG ≅ chord FH.

Fill in the blanks and write the proof.

Proof : Draw seg GF.

∠ EFG = ∠ FGH ...Alternate interior angles.......(I)

∠ EFG = …………90° ………{inscribed angle theorem}(II)

∠ FGH = …………… 90° ………….{inscribed angle theorem} (III)

∴m(arc EG) = ……………90°…………. from (I), (II), (III).

chord EG ≅ chord FH ..........

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