CircleHardBloom L3
Question
Tangents are drawn from $(4,4)$ to the circle $x^{2} + y^{2} - 2x - 2y - 7 = 0$ to meet the circle at $A$ and $B$. The length of the chord $AB$ is:
Options
A.$2\sqrt{3}$
B.$3\sqrt{2}$
C.$2\sqrt{6}$
D.$6\sqrt{2}$
Solution
[Key Concept: Tangents from $(4,4)$: chord of contact and tangent length from $\sqrt{S_{1}}$.]
$sin\theta = \frac{3}{3\sqrt{2}} = \frac{1}{\sqrt{2}}$
$$\theta = \frac{\pi}{4}$$
$$AB = 2rcos\theta = 2(3)\frac{1}{\sqrt{2}} = 3\sqrt{2}$$
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