Question

Line GJ is tangent to point A at point G.

If AG = 9 and GJ = 12, find AJ.

Answer 1

GJ is a tangent

АG is a radius

Step-by-step explanation: maybe

Answer 2

GJ is a tangent
АG is a radius
A tangent line to a circle is perpendicular to the radius drawn to the tangent point ⇒ m∠АGJ = 90° ⇒ ΔАGJ is the right triangle.

By the Pythagorean theorem:
AJ² = АG² + GJ²
AJ² = 9² + 12² = 81 + 144 = 225
AJ = √225 = 15 units.