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# 6.5 the incircle and circumcircle

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### 6.5 the incircle and circumcircle

1. 1. A. An In circle of a Triangle In Circle Angle bisectors can be used to construct an triangle In circle. Angle bisectors of a triangle intersect at a point called the In centre. In Center If a circle is constructed with the centre at the in centre, touching any one side, such a circle will touch the other two sides as well. This circle is called an in circle or inscribed circle.
2. 2. 1.Draw a triangle . Name the vertex of each angle. What is name of the triangle2.Tell the steps of drawing the in circle or inscribe circle of the triangle.
3. 3. B. Drawing an In circle of a Triangle Follow the steps to draw an in circle below: Steps 1. Draw a scalene triangle ABC. 2. Construct an in circle by locating the position of an in centre. Start with constructing an angle bisector of ∠A. a. Draw two small arcs from point A so that they intersect with the sides AC and AB. b. From the points of intersections of the arcs with the sides, draw two other arcs so that they intersect each other. c. Connect the point of the intersection of the arcs and point A with a straight line.
4. 4. B 3. Construct an angle bisector of ∠. a. Draw two small arcs from point B so that they intersect with the sides AB and BC. b. From the points of intersections of the arcs with the sides, draw two other arcs so that they intersect each other. c. Connect the point of the intersection of the arcs and point B with a straight line.
5. 5. 4. Construct an angle bisector of ∠B. a. Draw two small arcs from point C so that they intersect with the sides BC and AC. b. From the points of intersections of the arcs with the sides, draw two other arcs so that they intersect each other. c. Connect the point of the intersection of the arcs and point C with a straight line.
6. 6. 5.The three angle bisectors intersect at point O, the in circle. Draw a circle with O as its centre. It results in the in circle of the given triangle.
7. 7. C. An Circum circle of a Triangle Medians can be used to construct an Circum circle. Medians of a triangle intersect at a point called the center. Circum circle The Center This circle is called an circum circle or Circumscribed.
8. 8. 1.Draw a triangle . Name the vertex of each angle. What is name of the triangle2.Tell the steps of drawing the circum circle or circum circle of the triangle.
9. 9. C. Drawing an Circum circle of a Triangle Follow the steps below to draw a circum circle: Steps 1. Draw a scalene triangle ABC. 2. Locate the circum centre. A circum centre is the point of intersection of the medians of the sides of a triangle. Let us start by constructing a median of side AB. a. Open your compass to the width slightly larger than half of side AB. b. Draw two small arcs from A and B so that they intersect each other. c. Connect the points of intersection of the arcs with a straight line.
10. 10. 3.Let us start by constructing a median of side AC. a. Open your compass to the width slightly larger than half of side AC. b. Draw two small arcs from A and C so that they intersect each other. c. Connect the points of intersection of the arcs with a straight line.
11. 11. 4.Let us start by constructing a median of side BC. a. Open your compass to the width slightly larger than half of side BC. b. Draw two small arcs from B and C so that they intersect each other. c. Connect the points of intersection of the arcs with a straight line.
12. 12. 5. The three medians intersect at point O, the circum centre. Draw a circle with O as its centre. It results in the circum circle of the given triangle.
13. 13. An in circle of a triangle is a circle touching all parts awithin a triangle, where the center of the circle isinside the triangle.The center of an in circle of a triangle is the point ofintersection of three angle bisectors within the triangleA circum circle of triangle is a circle passing thoughtall Vertices triangle of a triangle. The center ofcircum circle can be either inside or outside triangle.The center of an circum circle of at triangle is thepoint of intersection of the three median within thetriangle.
14. 14. 1.Draw a triangle . Name the vertex of each angle. What is name of the triangle2.Tell the steps of drawing the in circle or inscribe circle of the triangle.3.Tell the steps of drawing the circum circle or circum circle of the triangle.
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