Q. 65.0( 3 Votes )

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Answer :

Formula used.

⇒ Perpendicular to tangent pass through centre of circle

⇒ Mid-point of chord is perpendicular line passes through centre

Solution.

As we join the figure

If P is mid-point of chord YZ

Then;

Line passing through centre to mid-point of line is perpendicular

Therefore OP is perpendicular to YZ

∠P = 90°

As there is tangent from point A on circle

Line passing through centre and point of contact is perpendicular to tangent

∠A = 90°

In Quadrilateral XAOP

∠A + ∠P = 90° + 90° = 180°

∠A + ∠P + ∠O + ∠X = 360°

∠O + ∠X = 360° - 180° = 180°

Sum of both opposite angles are 180°

∴ Quadrilateral XAOP is cyclic quadrilateral

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