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Step-by-step explanation:
(i) Given, Ab is a side of a regular hexagon.
So, Angle formed by it on the centre = 360°/6 = 60°.
So, Angle AOB = 60°
NOW,
Angle BOC = 180° - 60° = 120°
Angle BDC = Angle BOC/2 = 120°/2 = 60°
(We know that angle formed in a segment is half of the angle formed at the centre.)
(ii) In Triangle APB,
Angle PAB = 180°- Angle OAB = 180°-60° = 120°
Angle OBP = 90°
Angle ABO = 60°
Angle ABP = 90°-60° = 30°
Angle APB = 180°-120°-30° = 30°
Angle APB = Angle ABP
Hence, APB is an isosceles triangle.
Note: I have left some steps which are understood.
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