prove that angles in the same segment of circles are equal
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Explanation: Angles which are in the same segment are equal, i.e. angles subtended (made) by the same arc at the circumference are equal, The angles which are within a semicircle add up to 90°, ... Alternate Segment Theorem, i.e. that the angle between a tangent and its chord is equal to the angle in the 'alternate segment'.
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Answer:
Given - A circle with centre at O .
To Prove - angle poq = 2 angle paq .
Proof - angle poq = angle paq -------- 1.
Similarly
POQ =2 PBQ
From 1
2 PBQ = 2 PAQ
Angle PBQ = Angle PAQ
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