<p>The points $A(7,-6)$, $B\left( 9,2 \right)$ and $C\left( 1,4 \right)$ lie on a circle as shown in the diagram.</p>
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<ol class="abc-list"><li><div class="list-item-paragraph">Find the gradients of $AB$ and $BC$ and show that $AC$ is the diameter of the circle.</div></li><li><div class="list-item-paragraph">Find the coordinates of the centre of the circle and find the radius of the circle.</div></li><li><div class="list-item-paragraph">Find the equation of the circle.</div></li><li><div class="list-item-paragraph">Find the equation of the perpendicular bisector of $BC$ and determine whether it passes through the centre of the circle.</div></li></ol>

The points $A(7,-6)$, $B\left( 9,2 \right)$ and $C\left( 1,4 \right)$ lie on a circle as shown in the diagram.

Find the gradients of $AB$ and $BC$ and show that $AC$ is the diameter of the circle.

Find the coordinates of the centre of the circle and find the radius of the circle.

Find the equation of the perpendicular bisector of $BC$ and determine whether it passes through the centre of the circle.

Coordinate Geometry

Question 7920b362

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