Introduction:
The given statement states that the tangents drawn at the endpoints of a chord of a circle make equal angles with the chord. In order to prove this, we can use the properties of tangents and chords of a circle.

Proof:
Let's consider a circle with center O. Suppose AB is a chord of the circle, with points C and D as its endpoints. We need to prove that the angles ∠ACB and ∠ADB are equal.

Construction:
1. Draw tangents from points C and D to the circle, meeting the circle at points E and F respectively.
2. Join points A, B, and O to form radii of the circle.

Proof of ∠ACB = ∠ADB:
1. In △OEC and △OFD:
- OE = OF (Tangents drawn from the same point to a circle are equal in length).
- OC = OD (Radii of the same circle are equal).
- ∠OCE = ∠ODF (Both are right angles as they are tangents to the circle).
Therefore, △OEC ≅ △OFD (Side-Angle-Side congruence).

2. From the congruence of △OEC and △OFD, we can conclude that:
- ∠OEC = ∠OFD (Corresponding angles of congruent triangles are equal).

3. In quadrilateral ACBE, the sum of angles is 360 degrees. Hence, we have:
- ∠ACB + ∠CBE + ∠BEC + ∠ECA = 360 degrees.

4. Since ∠CBE and ∠BEC are both right angles (tangents to the circle), their sum is 180 degrees. Therefore:
- ∠ACB + 180 degrees + ∠ECA = 360 degrees.

5. Simplifying the equation, we get:
- ∠ACB + ∠ECA = 180 degrees.

6. From step 1, we know that ∠ECA = ∠OFD. Substituting this in the equation from step 5, we get:
- ∠ACB + ∠OFD = 180 degrees.

7. Rearranging the equation, we have:
- ∠ACB = 180 degrees - ∠OFD.

8. Similarly, we can prove that ∠ADB = 180 degrees - ∠OCE.

9. Since ∠OCE = ∠OFD (from step 1), we can conclude that:
- ∠ACB = ∠ADB.

Therefore, the tangents drawn at the endpoints of a chord of a circle make equal angles with the chord, and the statement is proven.