Question

Robbie wants to construct an equilateral triangle. He draws a diameter of circle O and constructs the perpendicular bisector of the diameter. He finds the points X and Y. Then he draws the triangle. What error did he make? Circle centered at O with diameter AB. An arc centered at A is drawn, intersecting the circle at two points. Another arc centered at B is drawn, intersecting the circle at the same points labeled X and Y outside the circle. XA and XB are joined. The first mistake Robbie made was ______. He should have ______.

1) not drawing the perpendicular bisector
2) not finding the points X and Y
3) not drawing the arcs centered at A and B
4) not joining XA and XB

Answer 1

Robbie made a mistake in constructing an equilateral triangle by joining the wrong points. To correct this, he should join the intersection points of the arcs with the circumference of the circle to form an equilateral triangle.

Step-by-step explanation:

Robbie's goal was to construct an equilateral triangle. If Robbie draws a diameter of a circle and the perpendicular bisector of that diameter, as well as find points X and Y by drawing arcs centered at A and B, the first mistake Robbie made was not constructing the triangle using the correct points. The second step to constructing an equilateral triangle should be to use the intersection points of the arcs with the circle to form the vertices of the equilateral triangle; not just connecting XA and XB. To draw an equilateral triangle, Robbie should utilize the intersections of the arcs with the circumference of the circle, which will be equidistant from each other, ensuring that all sides of the triangle are equal in length.

Therefore, the correct answer is that Robbie should have joined the points on the circle intersected by the arcs, instead of the points outside the circle. This will create an equilateral triangle inscribed in the circle.