if the power of point A with respect to the circle M of raidus 6 cm , equals 64 cm , then AM equal
The power of a point A with respect to a circle is given by the formula:
Power of A = (AM)(AM - r)
Where AM is the distance from point A to the center of the circle, and r is the radius of the circle.
Given that the power of point A with respect to circle M is 64 cm, and the radius of circle M is 6 cm, we can substitute these values into the formula:
64 = (AM)(AM - 6)
Expanding the equation and rearranging terms, we get:
AM^2 - 6AM - 64 = 0
This is a quadratic equation. We can solve it by factoring or using the quadratic formula. Factoring the equation, we get:
(AM - 8)(AM + 8) = 0
Setting each factor equal to zero, we get:
AM - 8 = 0 or AM + 8 = 0
Solving for AM in both equations, we find:
AM = 8 or AM = -8
Since distance cannot be negative, we discard the solution AM = -8. Therefore, AM = 8 cm.
So, AM is equal to 8 cm.