CAT Exam Model Paper 6 with solutions for free online practice

Question : 2 of 60

Marks: +1, -0

There are two concentric circles of radii 7 cm and 8 cm. PQ, a diameter of the larger circle, cuts the smaller circle at S and T. A tangent drawn from Q touches the inner circle at R. What is the length of PR (in cm)?

$√222$
$√211$
$√241$
None of these

Validate

Solution:

\R \Q = √{ 8 ^ { 2 } - 7 ^ { 2 } } = √ { 15 } { \cm }

.... (Pythagoras theorem)
In ∆(RPQ):

\PR ^ { 2 } + \RQ ^ { 2 } = 2 ( \O \R ^ { 2 } + \OQ ^ { 2 } ) ...

....(Apollonius' theorem)

\P \R ^ { 2 } = 2 ( 7 ^ { 2 } + 8 ^ { 2 } ) - 15

= 2 ( 49 + 64 ) - 15

⇒

\P \R ^ { 2 } = 211

\P \R = √{ 211 } { \cm }

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