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Question

If C1 and C2 are 2 circles with O and C as centres respectively and AB∥DE, then identify which angle is 50°.

A
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B
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C
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Solution

The correct option is A
Given that, C1 and C2 are circles with centres O and C respectively.
AB is the diameter of C1. A triangle inscribed in a semi circle with its diameter as the largest side will always be a right angled triangle.
ACB=90°

Angle subtended by an arc at the centre is double the angle subtended at the circumference.
DFE=12DCE=12×90°=45°

Since AB∥DE, DEC=40° [CPCT]
Using angle sum property in DCE,EDC=180°[DEC+DCE]
=180°[40°+90°]
=50°


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