Find the length of AB.

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Solution

Q.
The discus throw is an event in which an athlete aims to throw a discus as far as possible. The athlete spins counterclockwise one and a half times within a circle before releasing the discus. Upon release, the discus travels along a tangent to the circular path of the spin.

In the given figure, AB is one such tangent to a circle of radius 75 cm. Point O is centre of the circle and $∠ A B O = 30 ° .$ PQ is parallel to OA

Based on the above information answer the following questions:

(i) Find the length of AB.

1 $75 \sqrt{3} cm$

2 $75 \sqrt{2} cm$

3 $65 \sqrt{3} cm$

4 $- 75 \sqrt{3} cm$

Ans.
(1)

Since OA is radius and BA is tangent to the circle at point A

$∴ ∠ O A B = 90 ° I n Δ O A B, \tan 30 ° = \frac{O A}{A B} \Rightarrow \frac{1}{\sqrt{3}} = \frac{75}{A B} \Rightarrow A B = 75 \sqrt{3} c m$

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