SSC CHSL 13 Apr 2021 Shift 3 Paper

Section: Quantitative Aptitude

Question : 56 of 100

Marks: +1, -0

P, Q

and

R

are three points on the circumference of a circle such that

Q R

is a diameter and

P Q=P R

. If the radius of the circle is

7 {cm}

, then the length of

P Q

Solution:

Given,

Since, angle subtended by a diameter on the circumference of the circle is

90^{∘}

∴ \;\; ∠ Q P R=90^{∘}

Since,

P Q=P R=x

(let)

∴

△ P Q R

P Q^{2}+P Q^{2}=Q R^{2}

[by Pythagoras theorem]

⇒ x^{2}+x^{2}=(14)^{2}

⇒ \;\; (√{2} x)^{2}=(14)^{2}

⇒ \;\; x=\;{14}/{√{2}} × \;{√{2}}/{√{2}}=7 √{2}

∴ \;\; P Q=7 √{2} {cm}

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