**Q) **The discus throw is an event in which an athlete attempts to throw a discus. The athlete spins anti-clockwise around one and a half times through a circle, then releases the throw. When released, the discus travels along tangent to the circular spin orbit.

In the given figure, AB is one such tangent to a circle of radius 75 cm. Point O is centre of the circle and ZABO =30″. PQ is parallel to OA.

Based on above information:

(a) find the length of AB.

(b) find the length of OB.

(c) find the length of AP.

OR

Find the length of PQ

**Ans:**

**VIDEO SOLUTION**

**STEP BY STEP SOLUTION**

__(__i) __Value of line AB:__

In ΔOAB, tan 30° =

=

**AB = 75√3 cm**

**(ii) Value of line OB: **

In ΔOAB, Sin 30° =

=

OB = 75 x 2

**OB = 150 cm**

**(iii) Value of line AP: **

Now, given that radius OA = OQ = 75 cm

therefore, QB = OB – OQ = 150 -75 = 75 cm

Therefore, Q is midpoint of line OB

Given that PQ ǁ AO, and since, we just found that Q is midpoint of line OB,

Therefore, P is midpoint of AB.

Hence AP = =

**AP = **** cm**

**OR**

__Value of line PQ: __

__Method 1: __

We have just found out that OQ = QB = 75 cm

Now, In ΔQPB, Sin 30° =

=

PQ = =

**PQ = **** cm **

__Method 2: __

In ΔOAB and ΔQPB

OQ = QB, AP = PB, ∠OBA = ∠QBP

Therefore, ΔOAB ~ ΔQPB

=

=

**PQ = cm**