∫BC = BC’。

∴∠bc'c=∠bcc'； And < ∠a' c' b =∠ACB = 90°.

∴∠A'C'D=∠ACE (complementary angles of equal angles are equal)

∫A ' c ' = AC； ∠A ' DC ' =∠AEC = 90°。

∴⊿A'DC'≌⊿AEC(AAS),A'D=AE

So A'DP≌AEP can easily prove that P is the midpoint of AA'

Because the ratio of 30 degrees is CB/BA= 1/2.

C'BC is similar to A'BA, so C'C= 1/2A'A=AP.

The second question is the same, CB/BA= 1/ root 2.

C'C= 1/ root 2A'A= root 2AP