Question : In a circle with centre $O$ and diameter $E F$, if the two chords $A E=A F$, then $ \angle A E F$ is:
Option 1: 80°
Option 2: 90°
Option 3: 45°
Option 4: 60°
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Correct Answer: 45°
Solution :
In a circle with centre O and diameter EF, if the two chords AE = AF, then they form an isosceles triangle.
Also, we know that the angle in a semicircle is 90°.
$⇒\angle EAF = 90°$
Let $\angle AEF = \angle AFE = x$
Since the sum of angles in a triangle is 180°.
$⇒x+x+\angle EAF = 180°$
$⇒2x+90° = 180°$
$⇒2x=90°$
$⇒x=45°$
So, $\angle AEF = 45°$
Hence, the correct answer is 45°.
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