Mathematics 10 — Exercise 8.1 · Q2

Full question

Three steel rods are fixed at non-collinear points A,B,C. How many circular hoops can pass through all three?

Step-by-step solution

1. The points are not on one straight line.

2. The perpendicular bisectors of AB and BC meet at a unique point O.

3. O is equally distant from A,B,C. A circle centred there with radius OA passes through all three.

4. Any other centre would also have to lie on both perpendicular bisectors, forcing it to be the same O.

Answer

Exactly one hoop.