Question

19. The radii of two circles are 8 cm and 12 cm, while the distance between their centres is 15 cm. In how many point/s do these circles intersect ?​

Answer 1

Answer:

The circles will be intersecting in 2 points.

Step-by-step explanation:

Two circles can intersect each other either in one point or two point. We can say two circles intersecting in infinite points if they have same radius and center. Also we can say two circles are not intersecting, if the distance between their centers is greater the sum of their radii.

Following are the thumb rule:

⇒ Two circles does not intersect each other if the distance between their centers is greater than the sum of their radii.

⇒Two circles intersect in only one point, if the distance between their centers is exactly equal to the sum of their radii.

⇒Two circles intersect each others in two points, the distance between their centers is less than that of the sum of their Radii,

Given that the Radii of two circles are $8cm$ and $12 cm$ respectively.

Thus, Sum of Radii = $8+12=20cm$

Given that the Distance between their centers is $15cm$.

Clearly, the distance between the centers of given two circles is less than that of the sum of their radii.

Hence, given two circles will be intersecting in Two points.