How will you prove the theorems on secant tangent and segments of a circle?

If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

How do you prove tangent segment Theorem?

Proof of tangent segment theorem.

1. Statement: The segments of the tangent drawn from a point outside (external point) to a circle are congruent.
2. Proof:
3. Construction: Draw two segments AP and AQ.
4. According to the figure, A is the centre of the circle.
5. In ∆PAD and ∆QAD,
6. seg PA ≅ [segQA] [Radii of the same circle]

What is secant Theorem?

If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

What is the Secant tangent product theorem?

The Secant-tangent product theorem states that for any secant segment and tangent segment of a circle that meet at a common endpoint outside of the circle, it must be the case that: (Length of the whole secant segment)(Length of the external secant segment) = (Length of the tangent segment)2.

What is tangent secant segment Theorem?

The tangent-secant theorem describes the relation of line segments created by a secant and a tangent line with the associated circle. This result is found as Proposition 36 in Book 3 of Euclid’s Elements. The tangent-secant theorem can be proven using similar triangles (see graphic).

What is secant theorem?

What is tangent secant segment theorem?

What is a tangent and what is a secant?

A tangent line just touches a curve at a point, matching the curve’s slope there. (From the Latin tangens “touching”, like in the word “tangible”.) A secant line intersects two or more points on a curve. ( From the Latin secare “cut or sever”) They are lines, so extend in both directions infinitely.