Geometry_1

Geometry Level 2

$AB$ and $AC$ are the two tangents to a circle whose radius is $6$ cm. If $\angle BAC = 60^{\circ}$ , then what is the value (in cm) of $\sqrt{|AB|^{2} + |AC|^{2}}$ ?

9 \sqrt{3}

8 \sqrt{3}

4 \sqrt{6}

6 \sqrt{6}

1 solution

Edwin Gray
Jul 7, 2018

By symmetry, and the Pythagorean Theorem, each leg squared = 144 - 36 = 108, so the answer id sqrt(216) = sqrt(36*6) = 6sqrt(6). Ed Gray

Geometry_1

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