Theory question 102
Coordinate GeometryPoints (2, 1) and (6, 7) are opposite verticals of a square which is inscribed in a circle. Find the: (a) centre of the circle; (b) equation of the circle.
Show the model answer
Model answer
The diagonal of the square is a diameter.
(a) Centre = midpoint = (4, 4).
(b) r² = (2 − 4)² + (1 − 4)² = 13. (x − 4)² + (y − 4)² = 13, i.e. x² + y² − 8x − 8y + 19 = 0.
Explanation
A square's diagonal is a diameter of its circumscribed circle.