Practice Problems on Tangent Secant Theorem

Problem 1: In a circle with a radius of 5 cm, point P is located 13 cm away from the center O. A tangent is drawn from point P to the circle, and it touches the circle at point T. Calculate the length of PT.

Problem 2: In a circle with a radius of 8 cm, a secant is drawn from an external point P. The external portion of the secant is 12 cm, and the entire secant is 16 cm long. Find the length of the tangent segment from point P to the circle.

Problem 3: In a circle with a radius of 6 cm, a secant line is drawn from an external point P such that the tangent segment formed from P to the circle is 8 cm long. Find the length of the entire secant.

Problem 4: In a circle with a radius of 10 cm, a tangent is drawn from an external point P. If the tangent segment PT is 6 cm long, find the length of the secant from P to the circle.

Problem 5: In a circle with a radius of 7 cm, a secant is drawn from an external point P such that the external portion of the secant is 15 cm long, and the entire secant is 20 cm long. Calculate the length of the tangent segment from point P to the circle.

Problem 6: In a circle with a radius of 12 cm, point P is located 19 cm away from the center O. A tangent is drawn from point P to the circle, and it touches the circle at point T. Calculate the length of PT.

Tangent Secant Theorem is the fundamental theorem in geometry. Tangent and secant are the important parts of the circle. The tangent secant theorem is used in various fields of mathematics, construction, and many more. Tangents and secants are the lines that intersect the circle at some points.

In this article, we will learn about the Tangent Secant theorem in detail along with its statement and proof. It also covers the applications and limitations of the tangent secant theorem and some solved examples of the Tangent Secant Theorem. Let’s start our learning on the topic Tangent Secant theorem.