In the figure, O is the centre of the circle with radius r and P(a,b) is a point on the circle. AB is the diameter of the circle.  a) Prove that a2+b2=r2 b) Prove by the analytic approach that AP is perpendicular to PB.

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Chapter2: Second-order Linear Odes
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In the figure, O is the centre of the circle with radius r and P(a,b) is a point on the circle. AB is the diameter of the circle. 

a) Prove that a2+b2=r2

b) Prove by the analytic approach that AP is perpendicular to PB.

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