# Related Rates

Calculus Level pending

Two lines intersect at $$O$$ making an angle of $$2 \theta$$ between them, where $$\theta =30^{\circ}$$. $$T$$ is a point on their angle bisector that is $$a = 5$$ units away from $$O$$. Point $$A$$ is on one line and point $$B$$ is on the other line such that $$A$$ , $$T$$ and $$B$$ are collinear.

If point $$A$$ is moving with constant speed of 1 unit per second towards point $$O$$. How fast is point $$B$$ moving away from point $$O$$, at the instant when $$x = | OA | = 5$$?