In figure 3.61, chords AC and DE intersect at B. If ∠ ABE = 108°, m(arc AE) = 95°, find m(arc DC).

In figure 3.59, altitudes YZ and XT of

∆ WXY intersect at P. Prove that,

(1) WZPT is cyclic.

(2) Points X, Z, T, Y are concyclic.

In figure 3.60, m(arc NS) = 125°, m(arc EF) = 37°, find the measure ∠ NMS.

In figure 3.77, ray PQ touches the circle at point Q. PQ = 12, PR = 8, find PS and RS.

In figure 3.78, chord MN and chord RS intersect at point D.

(1) If RD = 15, DS = 4, MD = 8 find DN

(2) If RS = 18, MD = 9, DN = 8 find DS