Points $C$ and $E$ lie on opposite sides of chord $AB$, on the circle. $\angle ACB=37^\circ$

Question

Points $C$ and $E$ lie on opposite sides of chord $AB$, on the circle. $\angle ACB=37^\circ$. A pupil says that $\angle AEB=37^\circ$ because both angles stand on chord $AB$. Explain why the pupil cannot use the same-segment property.[1] Find $\angle AEB$, giving a reason.[2]

Accepted Answer

(a) Opposite sides of the chord (b) $143^\circ$

Checking the side-of-chord condition

Checking the side-of-chord condition

Solution:

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