The Question : 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.
Solution for the question :
∵ 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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