What is the length of RP?

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Solution

Q.
The diagram alongside shows a trapezium enclosed within a circle with a radius of 3 cm.

The length of AD is 5.5 cm and length of BC is 4 cm.

Based on the above information, answer the following questions:

(i) What is the length of RP

1 $\sqrt{5} cm$

2 $\sqrt{4} cm$

3 $\sqrt{1} cm$

4 $\sqrt{2} cm$

Ans.
(1)

We have radius of the circle PC = 3 cm, r = 3 cm

$A l s o, A B C D i s a t r a p e z i u m s u c h t h a t A D ∥ B C a n d B C = 4 cm$

$PR bisects the chord BC of the circle because PR ⟂ BC .$

$BR = RC = 2 cm In right triangle ∆ PRC, we have : {PC}^{2} = {PR}^{2} + {RC}^{2}$

$(3)^{2} = {PR}^{2} + (2)^{2} 9 = {PR}^{2} + 4 {PR}^{2} = 5 \Rightarrow PR = \sqrt{5} cm$

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