Multiple choice

In a circle with center O, ABCD is a cyclic quadrilateral and AC is the diameter. Chords AB and DC are produced to meet at E. If ∠CAE = 34o and ∠E = 30o , then ∠CAD is equal to?

  1. 36o

  2. 26 o

  3. 24 o

  4. 34 o
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a cyclic quadrilateral with diameter AC, angle ABC is 90 degrees (angle in a semicircle). In triangle ACE, angle ACE = 180 - (34 + 30) = 116 degrees. Since angle ACD = 180 - 116 = 64 degrees, angle CAD = 90 - 64 = 26 degrees using triangle angle sum property in right triangle ACD.

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