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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.

In the following figure, line DG is tangent to point A at F; line EC and line EH are-example-1

1 Answer

2 votes
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 .
User Prahalad Deshpande
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