MPM2D: Lesson 10 Quiz (K: 9, T: 16, C: 10)

1. A circle has a centre of (0,0) and a radius of 13.

1. Use Desmos.com to create a circle with a centre of (0,0) and a radius of 13 and save the file. The file name must be named so it starts with U2L10 followed by your name (eg. U2L10_Joseph). (K: 5)
2. The points A(0, _ ) , B( _ ,0) and C( _ , _ ) are points on the circle. From the graph on Desmos, determine a possible value to fill in each blank for each point. The point C must not contain any zeroes in its coordinates. (T: 3)
3. Construct the chords AB and AC. (C: 2)
4. Construct the perpendicular bisectors of the chords. (C: 4)
5. Construct the intersection of the perpendicular bisectors of the chords. Where do the chords intersect? (C: 4)
6. Save the file with all of the constructions completed.

2. A circle with a centre of (0,0) is defined by the equation x ²Â +y ²Â = 100.

1. Determine the radius of the circle. (K: 4)
2. The points A(0, _ ) , B( _ ,0) and C( _ , _ ) are points on the circle. Determine a possible value to fill in each blank for each point. The point C must not contain any zeroes in its coordinates. Provide calculation to show the points lie on the circle. (T: 3)
3. Use analytic geometry to determine the equations of the perpendicular bisectors of the chords AB and AC. (T: 6)
4. Show that the point (0,0) is the intersection of the perpendicular bisectors. (T: 4)