Question

So lies in the circumference of the circle. P (1, 3) is the centre of a circle and a point Q (7, 11) is any point in its circumference. Find the diameter of the circle. Does another point (-5, 10) lie in the circumference of the circle? ​

Answer 1

The diameter of the circle is 10. The point (-5, 10) does not lie on the circumference of the circle.

Step-by-step explanation:

To find the diameter of the circle, we need to find the distance between the center point P and any point on the circumference, such as Q. We can use the distance formula to calculate the distance.

The formula is: d = √[(x2 - x1)^2 + (y2 - y1)^2] Where (x1, y1) represents the coordinates of P and (x2, y2) represents the coordinates of Q. Plugging in the values, we get: d = √[(7 - 1)^2 + (11 - 3)^2] = √[(6)^2 + (8)^2] = √[36 + 64] = √100 = 10. Therefore, the diameter of the circle is 10.

To check if another point (-5, 10) lies in the circumference of the circle, we can calculate the distance between the center P and the point. Using the same distance formula, we get: d = √[(-5 - 1)^2 + (10 - 3)^2] = √[(-6)^2 + (7)^2] = √[36 + 49] = √85.

Since this distance is not equal to the diameter (10), the point (-5, 10) does not lie on the circumference of the circle.