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In a circle, the chord ED is parallel to the diameter AC, and angle CBE = 50 degrees (B is a point on the circle). Find angle CED.

1. 40 degrees
2. 50 degrees
3. 30 degrees
4. 60 degrees

Correct answer: 40 degrees

Solution

Angle CBE and angle CAE subtend the same arc CE, so angle CAE = angle CBE = 50 degrees. Since AC is a diameter, the angle in the semicircle angle AEC = 90 degrees. In triangle AEC, angle ACE = 180 - 90 - 50 = 40 degrees. Because ED is parallel to AC, the alternate angle gives angle CED = angle ACE =... actually angle DEC = angle ECA (alternate angles with transversal EC) = 40 degrees. Hence angle CED = 40 degrees.

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