Proof:

Let us consider two intersecting circles with centers O1 and O2, and let the common chord of the circles be AB. To prove that the tangents drawn from any point on the common chord to the circles are equal, we can follow the following steps:

Step 1: Mark the centers of the circles
- Let O1 be the center of the first circle and O2 be the center of the second circle.

Step 2: Draw the common chord AB
- Draw a line segment AB that intersects both circles at points P and Q.

Step 3: Draw tangents from point P to the circles
- Draw a line segment PC from point P to the first circle, perpendicular to AB.
- Draw a line segment PD from point P to the second circle, perpendicular to AB.

Step 4: Draw tangents from point Q to the circles
- Draw a line segment QE from point Q to the first circle, perpendicular to AB.
- Draw a line segment QF from point Q to the second circle, perpendicular to AB.

Step 5: Prove that the tangents from point P are equal
- Since PC and PD are radii of the first circle, they are equal in length. (PC = PD)
- Similarly, QE and QF are radii of the second circle, and they are also equal in length. (QE = QF)

Step 6: Prove that the tangents from point Q are equal
- Since QE and QF are radii of the second circle, they are equal in length. (QE = QF)
- Similarly, PC and PD are radii of the first circle, and they are also equal in length. (PC = PD)

Step 7: Conclusion
- From step 5 and step 6, we can conclude that the tangents drawn from any point on the common chord AB to the circles are equal in length.

Therefore, we have proved that the tangents drawn from any point on the common chord of two intersecting circles are equal.