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# Inscribed and circumscribed circles of a triangle

## 1. Inscribed and Circumscribed Circles of a triangle

“БІЛІМ-Инновация”Халықаралық қоғамдық қоры

CHAPTER no 4

GEOMETRY

Inscribed and

Circumscribed Circles of a

triangle

4-term

Week no 4

2019-2020

## 2.

CHAPTER no 4 Inscribed and Circumscribed Circles of a triangleYou will be able to:

know the definition of the inscribed and

circumscribed circles of a triangle;

explain the location of centers of circumference, for a

circle circumscribing a triangle and inscribed into a

triangle.

GEOMETRY

4-term

Week no 4

2019-2020

2

## 3.

CHAPTER no 4 Inscribed and Circumscribed Circles of a triangleKey terms:

Inscribed Circle – іштей сызылған шеңбер –

вписанная окружность

Circumscribed Circle – сырттай сызылған шеңбер –

описанная окружность

GEOMETRY

4-term

Week no 4

2019-2020

3

## 4.

CHAPTER no 4 Inscribed and Circumscribed Circles of a triangleReview:

Imagine triangle, in this triangle drawn 3 angle

bisectors from each vertices, and intersecting point

of all angle bisectors INCENTER

GEOMETRY

4-term

Week no 4

2019-2020

4

## 5.

CHAPTER no 4 Inscribed and Circumscribed Circles of a triangleDefinition:

A circle is INSCRIBED in the triangle if triangle’s

three sides are all tangent to the circle.

The center of the circle inscribed in a triangle is

incenter of a triangle.

GEOMETRY

4-term

Week no 4

2019-2020

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## 6.

CHAPTER no 4 Inscribed and Circumscribed Circles of a triangleExample:

Find the center of inscribed circle of a

triangle ABC.

Solution:

As we know, incenter is a center of inscribed circle

of a triangle. Let us use protractor to find half of

measure of each angle. We draw angle bisectors of

triangle ABC, like AM, BK and CH. The point E is a

center of inscribed circle of the triangle ABC

GEOMETRY

4-term

Week no 4

2019-2020

6

## 7.

CHAPTER no 4 Inscribed and Circumscribed Circles of a triangleDefinition:

A CIRCUMSCRIBED circle of a triangle

is a circle that passes through all the

vertices of the triangle.

A circumcenter of a triangle, the point

where the perpendicular bisectors of

the sides meet.

GEOMETRY

4-term

Week no 4

2019-2020

7

## 8.

CHAPTER no 4 Inscribed and Circumscribed Circles of a triangleExample:

Construct the circumcenter of the

triangle ABC.

Solution:

As we know, circumcenter of a triangle is a center of a

circumscribed circle of a triangle. And circumcenter is

intersecting point of perpendicular bisectors of the

sides. At firstly, we find midpoints of the each side of a

triangle using ruler, then, draw a perpendicular line to

midpoint of each side of a triangle.

GEOMETRY

4-term

Week no 4

2019-2020

8

## 9.

CHAPTER no 4 Inscribed and Circumscribed Circles of a triangleTask:

Draw three triangles of different shapes and then

construct the circle that circumscribes them. Next,

draw three triangles and then construct the circle

that inscribes them.

GEOMETRY

4-term

Week no 4

2019-2020

9

## 10.

CHAPTER no 4 Inscribed and Circumscribed Circles of a triangleResources:

https://www.onlinemathlearning.com/inscribed-circle.html

https://www.onlinemathlearning.com/inscribed-circumscribed-circles-hsg-c3.html

http://www.malinc.se/math/geometry/dothisen.php

GEOMETRY

4-term

Week no 4

2019-2020

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