In a circle with centre O, ABCD is a cyclic quadrilateral & AC is a diameter. Chords AB & CD are produced to meet at E. If ∠CAE = 34º and ∠E = 30º, then ∠CBD is equal to?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 26°
∠CAE = 34º and ∠E = 30º
∠ADC = 90º [Since AC is the diameter]
∠ACD = ∠CAE + ∠E [External angle theorem]
⇒ ∠ACD = 34 + 30 = 64º
Now,
∠DAC = 180 - (90 + 64) = 180 - 154 = 26º
Now, arc CD makes an angle 26° i.e. ∠DAC
We know that an arc subtends equal angles
Hence, ∠CBD = 26° (angles subtended by an arc are equal)