SATHEE: Quantitative Aptitude Ques 238

Quantitative Aptitude Ques 238

Question: ABC is a cyclic triangle and the bisectors of $ \angle BAC, $ $ \angle ABC $ and $ \angle BCA $ meet the circle at P, Q and R, respectively. Then, the $ \angle RQP $ is

Options:

A) $ 90{}^\circ -\frac{\angle B}{2} $

B) $ 90{}^\circ +\frac{\angle C}{2} $

C) $ 90{}^\circ -\frac{\angle A}{2} $

D) $ 90{}^\circ +\frac{\angle B}{2} $

Show Answer

Answer:

Correct Answer: A

Solution:

Here, RBPQ makes a cyclic quadrilateral.

$ \therefore $ $ \angle RQP+\angle RBP=180{}^\circ $ $ \angle RQP=180{}^\circ -\angle RBP $ (i) Now, $ \angle RBP=\angle RBA+\angle B+\angle CBP $ $ \angle RBP=\frac{\sqrt{C}}{2}+\angle B+\frac{\angle A}{2} $ (ii) Put value of $ \angle RBP $ in Eq. (i), we get $ \angle RQP=180{}^\circ -( \frac{\angle C}{2}+\angle B+\frac{\angle A}{2} ) $ $ =180{}^\circ -( \frac{\angle A+\angle B+\angle C+\angle B}{2} ) $ $ =180{}^\circ -( \frac{180{}^\circ +\angle B}{2} ) $ $ =180{}^\circ -90{}^\circ -\frac{\angle B}{2}=90{}^\circ -\frac{\angle B}{2} $

Quantitative Aptitude Ques 237

Quantitative Aptitude Ques 239

Quantitative Aptitude Ques 238

Question: ABC is a cyclic triangle and the bisectors of $ \angle BAC, $ $ \angle ABC $ and $ \angle BCA $ meet the circle at P, Q and R, respectively. Then, the $ \angle RQP $ is

Options:

Answer:

Solution:

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