Theorems on Secants of a Circle A secant of a circle is a line that intersects the circle at two distinct points. Secants play a crucial role in geometry, particularly in the study of circles and their properties. In this article, we will explore the theorems related to secants of a circle, including the Power of a Point Theorem, the Secant-Secant Theorem, and the Secant-Tangent Theorem. Power of a Point Theorem The Power of a Point Theorem states that if a point P is located outside a circle with center O, and a secant line passing through P intersects the circle at points A and B, then the product of the lengths of the segments PA and PB is equal to the square of the length of the tangent segment from P to the circle. Mathematically, this can be expressed as: PA × PB = PT^2 where PT is the length of the tangent segment from P to the circle. Proof of the Power of a Point Theorem The proof of the Power of a Point Theorem involves using similar triangles and the Pythago...