"Nature and Judgment of Tangent Lines" PPT

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"Nature and Judgment of Tangent Lines" PPT

Part 1: Positional relationship between straight lines and circles

1. Distinguish by the number of common points

Features: A straight line and a circle have two common points, which are called intersections of the straight line and the circle. The straight line at this time is called the secant of the circle.

Features: A straight line and a circle have the only common point, which is called tangent to the straight line and the circle.

The straight line at this time is called a tangent line, and the only common point is called a tangent point.

Features: A straight line and a circle have no common points, which is called a straight line and a circle that are separated from each other.

2. Use the relationship between the distance d from the center o of the circle to the straight line l and the radius r of the circle to distinguish

1. The straight line and the circle are separated by d > r

2. The straight line is tangent to the circle d = r

3. The straight line and the circle intersect d < r

The nature and judgment of tangents PPT, part 2: observation and thinking

Question 1: On a rainy day, in which direction do the water droplets on the rotating umbrella fly out?

Question 2: When the grinding wheel rotates, in what direction do the sparks fly out of the grinding wheel?

Give it a try

Draw a ⊙O and a radius OA, and draw a straight line l passing through the outer end point A of the radius OA of ⊙O and perpendicular to this radius OA. What is the distance from the center O of the circle to the straight line l? What is the positional relationship between straight line l and ⊙O?

The nature and determination of tangents PPT, the third part: knowledge induction

Determination theorem of tangent line

A straight line passing through the outer endpoint of a radius and perpendicular to the radius is a tangent to the circle.

condition:

(1) Passing through a point on the circle;

(2) Perpendicular to the point radius;

reasoning format

∵OA⊥l

∴The straight line l is the tangent line of ⊙ O

From this, do you know how to draw the tangent line of a circle?

Theorem of properties of tangent lines

The tangent to a circle is perpendicular to the radius passing through the tangent point.

Can you prove this theorem?

reasoning format

∵The straight line l is the tangent line of ⊙ O

∴OA⊥l

PPT on the nature and determination of tangents, part 4: summary of methods:

There are two common ways to prove that a straight line is a tangent to a circle:

(1) When the straight line and the circle have a common point, connect the center of the circle to the common point, and then prove that the straight line is perpendicular to this radius, which is referred to as "find the radius and prove perpendicularity".

(2) When the common point of the straight line and the circle is not clear, the perpendicular of the straight line can be drawn through the center of the circle, and then it is proved that the distance from the center of the circle to the straight line is equal to the radius, which is referred to as "draw the perpendicular and prove the radius".

Known: As shown in the figure, point A is a point outside ⊙O, OA intersects ⊙O at point B, AC is the tangent line of ⊙O, the tangent point is C, and ∠A=30°, AB=1. Find the radius of ⊙O

Method summary:

When the tangent line of a circle is known, the center point of the circle and the tangent point are often connected to obtain the radius perpendicular to the tangent line. The problem is solved by constructing a right triangle.

PPT on the nature and determination of tangents, part five: summary:

1. How to determine whether a straight line is a tangent to a known circle?

(1) A straight line that has only one common point with a circle is a tangent to the circle;

(2) The straight line whose distance from the center of the circle is equal to the radius is the tangent line of the circle;

(3) The straight line passing through the outer end of the radius and perpendicular to the radius is the tangent line of the circle;

A. Passing through a point on the circle;

B. Perpendicular to the radius;

2. What are the properties of tangents to a circle?

The tangent to a circle is perpendicular to the radius passing through the tangent point.

Keywords: Free download of mathematics PPT courseware for the second volume of the ninth grade of Hebei Education Edition, PPT download of the properties and determination of tangents, .PPT format;

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"Nature and Judgment of Tangent Lines" PPT courseware:

"The Nature and Determination of Tangent Lines" PPT Courseware Part One Contents: Course Test Points Test Points 1 Tangent lines to a circle Properties of tangent lines Tangent lines to a circle ________ pass through the tangent point Radius Corollary (1) A straight line passing through the center of the circle and perpendicular to the tangent line must pass ________ ; (2) Passing through the tangent point and perpendicular to...

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Update Time: 2024-10-17

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

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