# Grade 10, Academic (MPM2D)

Study Force Academy
Mathematics
Free
• 34 lessons
• 0 quizzes
• 7 week duration
• ##### Unit 4: Quadratic Relations

Most relations that you have studied in mathematics have been linear. However, many non-linear also exist in real life.

## Grade 10, Academic (MPM2D)

### Properties of Circles

This last lesson in this unit will demonstrate a few important properties of circles. When you first start learning about circles, you learn what radius and diameter mean. As a refresher, the diameter is the measurement across the circle passing through the center (shown below), while the radius is half that distance. Furthermore, a chord of a circle is a straight line segment whose endpoints both lie on the circle’s circumference (distance around the circle).

The first thing that you’ll watch is how a line segment drawn from the circle of a circle relates to a chord drawn between two points along the circle’s circumference. You’ll see that in a perfect circle, the line from the center to the chord is always at 90° to the chord, so they have slopes that are negative reciprocals.

Furthermore, our next video will show that you cannot determine the center of a circle from just two points on the circumference. Because the center can lie anywhere along the right bisector of a chord produced between two points, a third point is needed to verify.