CAT 2019 Shift 1 Paper

Question : 72 of 100

Marks: +1, -0

AB is a diameter of a circle of radius 5 cm. Let P and Q be two points on the circle sothat the length of PB is 6 cm, and the length of AP is twice that of AQ. Then the length,in cm, of QB is nearest to

Validate

Solution:

Refer to the figure below:

∠ A P B=∠ A Q B=90^{∘}

angle in a semicircle is a right angle
Also, let

A Q=x,

A P=2 x

In Right

∆ A P B

A P^{2}=A B^{2}-B P^{2}

⇒ A P^{2}=10^{2}-6^{2}=8^{2}

A P^{2}=A B^{2}-B P^{2} ⇒ A P=8 ⇒ 2 x=8

⇒ x=4

Similarly, in Right

△ A Q B

B Q^{2}=A B^{2}-A Q^{2}

⇒ B Q^{2}=10^{2}-4^{2}=84

⇒ B Q=√{84} ≈ 9.1

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