Question

In the following figure, line DG is tangent to point A at F; line EC and line EH are tangent segments. If A F = 11 and DF = 17, find AD

Round your answer to the nearest hundredth.

Answer 1

DG is the tangent
АF is the radius
A tangent line to a circle is perpendicular to the radius drawn to the tangent point ⇒ m∠АFD = 90° ⇒ ΔАDF is the right triangle (АD is the hypotenuse).

By the Pythagorean theorem:
АD² = АF² + DF²
АD² = 11² + 17² = 121 + 289 = 410
АD = √410 ≈ 20.25 units ← to the nearest hundredth.