Question

A circle with centre (3, 2) passes through the point (6,8) a) What is the radius of the circle b) check wheter each points with Coordinates (0,2) (3,6)(0,3) is inside or outside or on the circle
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Answer 1

ANSWER :

radius is

$3 \sqrt{5}$

the point (0,2) and (0,3) lies inside the circle

point (3,6) lies outside the circle

the circle passes through the point (6,8) means it lies on the circle

the distance from the centre to any point onthe circle gives radius of the circle

$\sqrt{(6 - 3) {}^{2} + (8 - 2) ^{2} } = 3 \sqrt{5}$

the radius of the circle is e square root of 5

the distance between (3,2) and (0,2)

$\sqrt{(3 - 0) ^{2} + (2 - 2) ^{2} } =3$

the distance between (3,2) and (3,6)

$\sqrt{(3 - 3) ^{2} + (6 - 2) ^{2} } = 4$

the distance between (3,2) and (0,3)

$\sqrt{(0 - 3) ^{2} + (3 - 2) ^{2} } = \sqrt{10}$

if the distance between 2 points is less than radius then the point lies inside the circle

3 and square root of 10 are less than radius so the points (3,2) and (0,2) lies inside the circle

if the distance between 2 points is greater than radius then the point lies outside the circle

4 is greater than radius so point (3,6) lies outside the circle