F.4 Maths

As follows:

圖片參考：http://i240.photobucket.com/albums/ff164/walkinginthesang/e64e2fe5.jpg?t=1194166905

I think you have missed out point B where AB is the diameter of the circle.
∠BPD + ∠BDP = ∠ DBA ( ext. ∠ of △ )
20* + 30* = ∠ DBA
∠ DBA = 50*
∠ DBA = ∠ DCA = 50* ( ∠s in the same segment )
∠ ADB = 90* ( ∠ in semi - circle )
∠ ADC + ∠ DCA + ∠ DAC = 180* ( ∠ sum of △ )
( 90* + 20* ) + 50* + ∠ DAC = 180*
∠ DAC = 20*
∠ DAC = ∠ CBD = 20* ( ∠s in the same segment )

∠ DAC = ∠ CBD = 20*