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 3.92, O is the centre of a circle, chord PQ ≅ chord RS If∠ POR = 70°and (arc RS) = 80°, find -

(1) m(arc PR)

(2) m(arc QS)

(3) m(arc QSR)

In figure 3.93, m(arc WY) = 44°,m(arc ZX) = 68°, then

(1) Find the measure of ∠ ZTX.

(2) If WT = 4.8, TX = 8.0,YT = 6.4, find TZ.

(3) If WX = 25, YT = 8,YZ = 26, find WT.

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 3.96 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.