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## Inscribing Shapes in Circles

#### High School Congruence - HSG-CO.D.13

What are Inscribed Shapes? - Do you like eggs? Then you surely know what they look like. Delicious and yummy with an outer white part and a yellow circular yolk fitting in the center. Do you know the geometrical term for figures like eggs? They are called inscribed shapes. Let's see what the term actually means. Any planar shape that fits into another shape is called an inscribed shape. To understand better, take a piece of paper and draw whichever shape you like. Triangle, square, rectangle, or any other shape. Next, draw another shape inside the shape you first drew such that it perfectly fits inside it. Now take a look. Can you see how one shaping is holding another inside of it? This image in front of you is now called an inscribed shape.

### Printable Worksheets And Lessons  #### Homework Sheets

I love to see the faces of kids when they see these problems for the first time. The skill looks unattainable, at first.

• Homework 1 - Mark a point anywhere on the circle. This will be the first vertex of the hexagon.
• Homework 2 - Start by constructing a circle. Construct a diagonal through this circle. Extend the diagonal beyond the circumference of the circle. Construct a perpendicular line to this line through the center.
• Homework 3 - Increase the compasses width, just a bit. Place the compass point where each arc crosses the side and draw two crossing arcs inside the triangle.

#### Practice Worksheets

Bisectors and circle geometry should have been mastered before students move on to these.

• Practice 1 - Construct the largest regular hexagon that will fit in the circle below.
• Practice 2 - Construct a regular pentagon that will fit in the circle below.
• Practice 3 - Draw the largest possible circle inscribed in this equilateral triangle.

#### Math Skill Quizzes

These quizzes are more artistic than anything else we have seen in this content area.

• Quiz 1 - Construct a regular square that will fit in the circle below.
• Quiz 2 - Get yourself a ruler and draw a line from the vertex of the triangle to the point where the two arcs cross.
• Quiz 3 - Construct a dodecagon that will fit in the circle below.