"Inscribed Circles of Triangles" PPT Courseware 3

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"Inscribed Circles of Triangles" PPT Courseware 3

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Definition of tangent length:

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

Tangent length theorem:

Two tangents to the circle can be drawn from a point outside the circle. Their tangents are of equal length. The line connecting this point to the center of the circle bisects the angle between the two tangents.

think

Xiao Ming works in a lumber factory. In his spare time, he wants to process the triangular waste materials in the factory: cut out a circular piece of material and maximize the area of ​​the circle.

The pictures below show several of his designs. Please help him identify them.

consolidate

1. The inscribed circle ⊙O of △ABC and each side are tangent to points D, E, and F respectively, then point O is ( ) of △DEF

A. The intersection of three heights

B. The intersection of three angle bisectors

C. The intersection of three midlines

D. The intersection of three perpendicular bisectors

2. As shown in the figure, l1, l2, and l3 are three highways. It is necessary to build a gas station inside a triangle so that the distance between the gas station and the three highways is equal. Where should the gas station be built?

Why?

3. As shown in the figure, ⊙O is the inscribed circle of Rt△ABC. The tangent points are D, E, and F respectively. The radius is r. ∠C=90°. The lengths of AB, BC, and CA are a, b, and c respectively. .

Prove: r=a+b-c/2

summary

1. Definition of inscribed circle of triangle

2. Definition of the center of a triangle

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For more information about the "Inscribed Circles of Triangles" PPT courseware, please click the Inscribed Circles of Triangles ppt tab.

"Inscribed Circles of Triangles" PPT Courseware 2:

"Inscribed Circles of Triangles" PPT Courseware 2 As shown in the picture, the carpenter wants to cut a circular piece from a triangular piece of wood. How can he make the area of ​​the cut circle as large as possible? Construct a circle so that it is tangent to all sides of the known triangle. Given: △ABC (as shown in the figure). Find the...

"Inscribed Circles of Triangles" PPT courseware:

"Inscribed Circles of a Triangle" PPT courseware. The picture shows a triangular piece of wood. The carpenter needs to cut a circular piece of material from it. How can the area of ​​the cut circle be made as large as possible? The circle that is tangent to all sides of a triangle is called the incircle of the triangle, and the triangle is called the circumference of the circle.

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Update Time: 2024-11-16

This template belongs to Mathematics courseware Qingdao Edition Ninth Grade Mathematics Volume 1 industry PPT template

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