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