XY and MN are the tangents drawn at the end points of the diameter DE of the circle with centre O. Prove that XY || MN - Maths

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XY and MN are the tangents drawn at the end points of the diameter DE of the circle with centre O. Prove that XY || MN.



XY is the tangent to the circle at the point D 

∴ OD ⊥ XY  ⇒ ∠ ODX = 90° ⇒ ∠ EDX = 90° 

Also, MN is the tangent to the circle at E 

∴ OE ⊥ MN ⇒ ∠ OEN = 90° ⇒ ∠ DEN = 90° 

⇒ ∠ EDX ∠ DEN (each 90°). 

which are alternate interior angles. 

∴ XY | | MN

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