Quantitative Aptitude Ques 1527

Question: Two chords AB and CD of a circle with centre O, intersect each other at P. If $ \angle AOD=100{}^\circ $ and $ \angle BOC=70{}^\circ , $ then the value of $ \angle APC $ is

Options:

A) $ 80{}^\circ $

B) $ 75{}^\circ $

C) $ 85{}^\circ $

D) $ 95{}^\circ $

Show Answer

Answer:

Correct Answer: D

Solution:

  • (d) In the given figure, $ \angle AOD=100{}^\circ $
    $ \Rightarrow $ $ \angle BOC=70{}^\circ $ Now, join AC.
    $ \angle ACD=\frac{1}{2}\angle AOD $ [since, angle subtended at the centre is twice the angle subtended on circumference of following circle] $ =\frac{1}{2}\times 100=50{}^\circ $ Similarly, $ \angle CAB=\frac{1}{2}\times \angle DOB=\frac{1}{2}\times 70{}^\circ =35{}^\circ $ In $ \Delta APC, $ $ \angle APC=180{}^\circ -\angle ACP-\angle CAB $ $ =180{}^\circ -50{}^\circ -35{}^\circ $ $ [\because \angle ACP=\angle ACD] $ $ =95{}^\circ $
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