Question

Milynn is constructing an inscribed triangle in a circle using technology. Circle A has points B, C, and D on the circle. Line BD intersects the circle at B and D and passes through the center of the circle at point A. Points B and C are located at the same place.

Part A: Where should Milynn place the center of the next circle? Explain your answer.
Part B: What should the radius of the next circle be? Explain your answer.

Answer 1

Milynn should place the center of the next circle at point A, which is already the center of Circle A for the construction. The radius of the next circle should equal the radius of circle A to ensure the vertices lie on the circumference, creating an inscribed triangle with the necessary geometric properties.

Step-by-step explanation:

Part A: Milynn should place the center of the next circle at point A, which is the center of the original circle. Since line BD passes through the center A and intersects the circle at B and D, creating a diameter, it suggests we are working with a central angle and inscribed angles. For an inscribed angle to intercept the diameter, it must be a right angle. Therefore, by placing the center of the next circle at point A, the new circle will allow us to locate point C such that triangle BCD will have a right angle at C.

Part B: The radius of the next circle should be the same as the radius of circle A. This is because point B (where points B and C are initially at the same place) is located at the circumference of the circle, and the distance from point A (center) to any point on the circle is consistent. Hence, by using the same radius, we can ensure that the triangle's vertices all lie on the circle's circumference, maintaining the properties of an inscribed triangle.