CAT 2018 Question Paper Shift 2 Solved Paper

Question : 91 of 100

Marks: +1, -0

On a triangle ABC, a circle with diameter BC is drawn, intersecting AB andAC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, is

Your Answer:

Validate

Solution:

Refer to the below diagram

Observe that triangle

{BPC}

and

{BQC}

are inscribed inside a semicircle. Hence,

∠ {BPC}=∠ {BQC}=90^{∘}

Therefore, we can say that

B Q ⟂ A C

and

C P ⟂ A B

.
Also, In triangle

{ABC}

,
Area of triangle

=(1 {/} 2) ×

Base

\times

Height

=(1{/} 2) × {AB} × {CP}=(1 {/} 2) × {AC} × {BQ}

⇒ {BQ}=\;{A B × C P}/{A C}=\;{30 × 20}/{25}=24 {cm}

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