Geometry mathematics question

Question

Given three points A, B, and C on a circle, with AB = 8, BC = 4, and CA = 6. Let D be a point outside the circle such that DC is tangent to the circle and ∠DCA < 90◦ . If DC = 12, find the length of AD.

Answer 1

Draw the diagram. You can see that there is a right triangle formed by DCA with the legs being DC and AC. You can find AD, the hypotenuse of the right triangle (side opposite the right angle) using Pythagorean Theorem.