A point p is 6.5cm from the centre of a circle and the length of the tangent from p is 5.6cm. calculate the radius of the circle.
Let's call the radius of the circle r. According to the given information, we have a right triangle formed by the radius, the tangent, and the distance from the center of the circle to the point.
Using the Pythagorean theorem, we can set up the equation:
(r)^2 = (6.5)^2 + (5.6)^2
r^2 = 42.25 + 31.36
r^2 = 73.61
Taking the square root of both sides, we find:
r = √73.61
r ≈ 8.57 cm
Therefore, the radius of the circle is approximately 8.57 cm.