"Tangent Line Length Theorem" PPT courseware

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"Tangent Line Length Theorem" PPT courseware

Part One: Concept of tangent length

Draw the tangent line of the circle through a point outside the circle. The length of the line segment between this point and the tangent point is called the length of the tangent line from this point to the circle.

tangent and tangent length

Tangent lines are straight lines and cannot be measured;

The tangent length is the length of a line segment. The two endpoints of this line segment are a point outside the circle and a tangent point, which can be measured.

Prove the conjecture

Based on your intuitive judgment, guess whether PA in the picture is equal to PB? What is the relationship between ∠1 and ∠2?

prove:

∵PA and PB are two tangent lines of ⊙o,

∴OA⊥AP,OB⊥BP

And OA=OB, OP=OP,

∴Rt△AOP≌Rt△BOP (HL)∴PA=PB, ∠1=∠2

Part 2 content: Tangent length theorem:

Two tangents to a circle drawn from a point outside the circle have equal tangent lengths, and the line connecting this point to the center of the circle bisects the angle between the two tangents.

Extension of tangent length theorem

(1) Write out all the vertical relationships in the figure

(2) Which line segments (except radii) and arcs in the figure are equal?

The center of the circumscribed circle: the intersection point of the perpendicular bisectors of the three sides of the triangle.

The radius of the circumscribed circle: the distance from the intersection point to any fixed point of the triangle.

The center of an inscribed circle: the intersection point of the three interior angle bisectors of a triangle.

Radius of inscribed circle: The vertical distance from the intersection point to any side of the triangle.

Tangent length theorem PPT, the third part: summary:

(1) Tangent length theorem.

(2) Connecting the center of the circle and the tangent point is a commonly used auxiliary line when we solve problems related to the tangent length theorem.

Keywords: Free download of mathematics PPT courseware for the second volume of the ninth grade of Hebei Education Edition, PPT download of tangent length theorem, .PPT format;

For more information about the "Tangent Length Theorem" PPT courseware, please click the "Tangent Length Theorem" ppt tag.

"Tangent Line Length Theorem" PPT:

"Tangent Length Theorem" PPT Part One Content: Problem Exploration Question 1. What will happen if a tangent line to a known circle is drawn through a known point on the plane? Question 2. How to draw a tangent line to a given ⊙O through a point P outside the circle? Thinking: Assume that the tangent line PA has been made, A..

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Update Time: 2024-10-18

This template belongs to Mathematics courseware Hebei Education Edition Ninth Grade Mathematics Volume 2 industry PPT template

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