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:

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

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