Simple circle question

Question

let AB be diameter of circle and AC be the chord. Let a tangent is drawn from C to meet AB produced at D.If BAC=30,Prove that BC= BD

SOLUTION

ACB= 90

ABC=60

CBD=120

After that I am confused

Answer 1

Remember the theorem about the angle between a tangent and a cord at the tangency point, so you get

$$\angle BCD=\angle CAB=30^\circ$$

Using now that $\;\angle CBD=120^\circ\;$, deduce $\;\Delta BCD\;$ is isosceles and you're done.