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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.

Tangent is Parallel to a Chord of a Circle

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.







10th Grade Math

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