# Tangent is Parallel to a Chord of a Circle

We will prove that, A tangent, DE, to a circle at A is parallel to a chord BC of the circle. Prove that A is equidistant from the extremities of the chord.

Solution:

Proof:

 Statement Reason 1. ∠DAB = ∠ACB 1. Angle between tangent and chord is equal to the angle in the alternate segment. 2. ∠DAB = ∠ABC 2. Alternate angles and DE  ∥ BC. 3. ∠ACB = ∠ABC 3. From statements 1 and 2. 4. AB = AC⟹ A is equidistant from B and C, the extremities of the chord. (Proved) 4. From statement 3.

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