Two chords AB and CD of a circle with ce

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Geometry

Question:

Two chords AB and CD of a circle with centre O intersect each other at P. If ∠AOD = 120° and ∠BOD = 50°, then the value of ∠APC is?

Options:

85°

75°

95°

100°

Correct Answer:

95°

Explanation:

∠AOD = 120°

∠ACD = \(\frac{1}{2}∠AOD\)

∠ACD = 60° = ∠ACP

∠BOC = 50°

∠CAB = \(\frac{1}{2}∠BOC\) = 25° = ∠CAP

Now, in ΔACP

∠APC = 180° - (∠ACP + ∠CAP)

∠APC = 180° - (60° + 25°)

= 180° - 85°

∠APC = 95°