Question

In the following figure, line DG is tangent to point A at F; line EC and line EH are tangent segments. If AH = 5 and AE = 13, find HE.

Answer 1

HE is the tangent
АH is the radius
A tangent line to a circle is perpendicular to the radius drawn to the tangent point ⇒ m∠АHE = 90° ⇒ ΔАHE is the right triangle.

By the Pythagorean theorem:
HE² = АE² - AH²
HE² = 13² - 5² = 169 - 25 = 144
HE = √144 = 12 units .