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Circular Measurement of Angle

Prove that th...

Question

Prove that the line segment joining the points of contact of two parallel tangents of a circle passes through its centre.

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Solution

$O A | | P Q ∠ P M O ∠ A O M = 180 ° (A d j a c e n t C) & ∠ P M O = 90 ° (T a n g e n t p e r p e n d i c u l a r t o R a d i i) \Rightarrow ∠ A O M = 90 ° = ∠ A O N \Rightarrow ∠ A O N + ∠ R N O = 180 °$
So, MON is straight line through $O$

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