In ΔPQR, the bisector of ∠QPR

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Geometry

Question:

In ΔPQR, the bisector of ∠QPR intersects QR at S and the circumcircle of ΔPQR at T. If PQ : PS = 3 : 5, then PT : PR is ?

Options:

3 : 5

5 : 3

1 : 1

2 : 5

Correct Answer:

3 : 5

Explanation:

Here,

∠PTQ = PRQ, (angle made by same chord PQ)

⇒ ΔPSR ∼ ΔPQT

⇒\(\frac{PS}{PR}\) = \(\frac{PQ}{PT}\)

⇒ \(\frac{5}{PR}\) = \(\frac{3}{PT}\)

= \(\frac{PT}{PR}\) = \(\frac{3}{5}\)