Draw a circle with 5cm radius. Inscribe a triangle with side ratio 5:6:7 in it.
so, draw the circle. The central angles subtended by the sides will be 100,120,140 degrees. It is easy to construct a 120° angle, so you can draw the side of length 6x first. Then from its ends draw arcs of radius 5x and 7x. They will intersect at the third vertex.
I got that wrong. The angles are not in the same ratio as the sides. The sines of the angles are.
So, you can still draw the triangle, but then you need to circumscribe it.
You can easily find online the relationship between the radius and the sides. In this case, with sides of 5,6,7 the radius is 35/(4√6) so just scale the sides appropriately.
To draw a circle with a 5cm radius and inscribe a triangle with a side ratio of 5:6:7 in it, you can follow these steps:
1. Start by drawing the circle with a 5cm radius. Take a ruler and draw a line that is exactly 5cm long. This will be the diameter of the circle. Use a compass to draw a perfect circle with the line as the diameter.
2. Once the circle is drawn, take a point on the circumference to serve as the starting point for the triangle. Mark this point with a dot.
3. To create a triangle with a 5:6:7 side ratio, draw a line segment from the starting point on the circle to create the first side of the triangle with a length of 5 units. Use a ruler for accuracy and draw the line from the dot on the circumference towards the center of the circle.
4. To determine the next two sides of the triangle, use some geometry principles. Since the triangle is inscribed in a circle, the other two sides must touch the circumference at some point. We can use the concept of angles formed by a chord and the radius of a circle.
5. With the compass, draw an arc from the starting point on the circle, intersecting the circumference on both sides of the first side (length 5 units). This creates two intersection points.
6. Draw two line segments from the starting point to each of the intersection points, creating the second and third sides of the triangle. Measure the lengths of these sides with a ruler, ensuring the lengths are in the ratio of 6:7.
7. Finally, connect the endpoints of the second and third sides of the triangle to close the shape, completing the inscribed triangle within the circle.
By following these steps, you should be able to draw a circle with a 5cm radius and inscribe a triangle with a side ratio of 5:6:7 in it.