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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°

A + P = 90° + 90° = 180°

A + P + O + X = 360°

O + X = 360° - 180° = 180°

Sum of both opposite angles are 180°

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