Please can someone give me the formula for this problem? All I need is the formula and then I can figure out the rest. Thanks!

Question

and  are tangent to Circle A. If mis 120°, find the value of ÐC.

Answer 1

1. Because arc BD is 120°, the measure of the corresponding central angle, ∠BAD, is also 120°. There is a circle theorem that states that a line from an external point to the center of a circle bisects the angle between the two tangents to the circle from the external point. So line AC bisects ∠BAD and m∠CAD = m∠CAB = 60°
2. Line AD is a radius and the radius is perpendicular to the tangent line, so m∠ADC = m∠ABC = 90°
3. Triangle ADC is thus a 30-60-90 right triangle where the three side lengths are in the ratio 1 : √3 : 2. That is, if AD = 1, then CD = √3, and AC = 2. So if AD = 5, for example, then DC = 5√3.