1. We use a compass to construct a circle with center O, of any - - PowerPoint PPT Presentation

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1. We use a compass to construct a circle with center O, of any - - PowerPoint PPT Presentation

Jan 29, 2023 428 likes •603 views

D AY 41 E QUILATERAL TRIANGLE INSCRIBED IN A CIRCLE I NTRODUCTION Some plane figures can draw inside a circle in such a way that the vertices touch the edge of the circle. For instance, a triangle can be drawn inside a circle such that all

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DAY 41 – EQUILATERAL

TRIANGLE INSCRIBED IN A CIRCLE

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INTRODUCTION

Some plane figures can draw inside a circle in such a way that the vertices touch the edge of the circle. For instance, a triangle can be drawn inside a circle such that all its three vertices touch the edge of the

  • circle. The common types of triangles can be drawn

inside a circle; however, in this lesson, we are going to learn how to construct an equilateral triangle inside a circle.

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VOCABULARY

Equilateral triangle A triangle that has all the three sides equal and all the three angles equal. Inscribed triangle A triangle is drawn inside another plane figure such that the vertices of the triangle touch the edge

  • f the plane figure, in this case, a circle.
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CONSTRUCTING AN EQUILATERAL

TRIANGLE INSCRIBED IN A CIRCLE We are going to construct an equilateral triangle inside a circle in such a way that its vertices touch the edge of the circle using a straightedge and a

  • compass. When a triangle is constructed inside a

circle as described above, we say that the triangle has been inscribed in the circle. The method used is based on the basic idea that a turn is equivalent to 360° and an equilateral triangle has all angles measuring 60°. Therefore, the circle is divided into six arcs each equivalent to 60°.

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To construct an equilateral triangle inscribed in a circle:

  • 1. We use a compass to construct a circle with center

O, of any convenient radius as shown below.

O

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  • 2. Using a straightedge, we draw a line segment

from the center to the edge of the circle as shown

  • below. We then label the other endpoint of the

segment P as shown below. OP is the radius of this circle.

O P

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  • 3. Using the same radius, we use point P as the

center and make an arc to intersect the circle. We label this intersection point Q as shown below.

O P Q

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  • 4. Using the same radius, we use point Q as the

center and draw an arc that intersects the circle at point R as shown below.

O P Q R

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  • 5. We continue to use the new intersection points

constructed as the new centers with the same radius until the last arc intersects point P as shown

  • below. We draw a total of 6 arcs.

O P Q R

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  • 6. We construct the sides of the equilateral triangle

by selecting any intersection point and joining it to the third intersection point using a straightedge as shown below. We repeat this process until the inscribed equilateral triangle is formed as shown below.

O P Q R

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Example Draw a circle of a suitable radius using a compass and construct an equilateral triangle inscribed in the circle with the help of a straightedge.

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Solution We draw a circle of any convenient radius and use the same radius to draw six arcs at equal intervals as shown below.

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We join the arcs with straight lines using a straightedge in the format shown below to form the inscribed triangle.

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HOMEWORK Use a pair of compasses and a straightedge to construct the largest possible equilateral triangle that will fit in the circle with center O shown below.

O

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ANSWERS TO HOMEWORK

The largest equilateral triangle drawn is the inscribed equilateral triangle. We use the center to get the radius.

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THE END