In this lesson, we will learn about inscribed angles in semicircles, circumcircles of triangles, and how to find the equation of a circle given three points on the circumference.

Students will be able to

Q1:

The points 𝐴(−3,−3), 𝐵(−5,−7), and 𝐶(−9,−3) lie on the circumference of a circle. The equation of the perpendicular bisector of 𝐵𝐶 is 𝑦=𝑥+2. Find the equation of the perpendicular bisector of 𝐴𝐵 and the coordinates of the center of the circle.

Q2:

The points 𝐴(3,−7), 𝐵(−12,−4), 𝐶(−8,4), and 𝐷(4,−4) lie on a circle. By finding the perpendicular bisectors of 𝐴𝐵 and 𝐶𝐷, write down the equation of the circle.

Q3:

𝐵(9,3), 𝐶(4,8), 𝐷(8,2), 𝐸(8,8), and 𝐹(3,7) are five points on a circle.

Which of the chords 𝐶𝐷, 𝐵𝐶, and 𝐷𝐹 is a diameter?

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