Question

what is the tangent second segment theorem?

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Answer 1

Answer:

The tangent-secant theorem describes the relation of line segments created by a secant and a tangent line with the associated circle.

For a secant g intersecting the circle in G1 and G2 and tangent t intersecting the circle in T that intersect in P the following equation holds:

{\displaystyle |PT|^{2}=|PG_{1}|\cdot |PG_{2}|}{\displaystyle |PT|^{2}=|PG_{1}|\cdot |PG_{2}|}

The tangent secant theorem can be proven using similar triangles (see graphic). Construct the diameter passing through point T, say it meets the circle at point D. Now, angles G1DT and G1G2T are equal because they subtend the same arc of the circle. Triangle G1DT is a right angled triangle because DT is diameter. Since, angle DTP is a right angle, angle PTG1 is equal to G1DT and hence equal to G1G2T. Now the similarity can be easily proved. Next to the intersecting chords theorem and the intersecting secants theorem it represents one of the three basic cases of a more general theorem about two intersecting lines and a circle - the power of point theorem.

Answer 2

Answer:

the angle between a chord and a tangent through one of the end points of the end points of the chord is equal to the angle in the alternate segment.

Step-by-step explanation: