Secant theorem: the tangent and secant of a circle are drawn from a point outside the circle, and the length of the tangent is the middle term in the length ratio of the two lines where this point intersects the secant. This is one of the cyclic power theorems.

Schematic diagram of cutting line theorem

Geometric language: ∵PT cuts ⊙ O at t point, and PDC is the secant of ⊙ o.

∴PT？ Secant theorem

Inference:

Draw two secants of a circle from a point outside the circle, and the product of the lengths of the two lines from that point to the intersection of each secant and the circle is equal.

Geometric language: ∵PT is the tangent of ⊙ O, and PBA and PDC are the secant of ⊙ O.

∴ PD PC = PA Pb (secant theorem inference) (secant theorem)

From top: PT? =PA PB=PC PD

certificate

Proof of cutting line theorem;

Let ABP be the secant of ⊙O, PT be the tangent of ⊙O, and the tangent point is T, then PT? =PA PB

Proof: connected to, BT

∫∠PTB =∣∠Pat (tangent angle theorem)

Proof of cutting line theorem

∠APT=∠TPA (male * * * angle)

∴△PBT∽△PTA (two angles are equal and two triangles are similar)

Then Pb: pt = pt: AP

Namely: PT? =PB PA

compare

Secant theorem, secant theorem, secant theorem (secant theorem inference) and their inferences are collectively called circular power theorem. Generally used to find the length of a straight line segment.