The required length from the point outside the circle to the point on the circle i.e. CE is 8 and the length from the point outside the circle to the center is 13.
What is a circle?
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
where h, k is the coordinate of the center of the circle on coordinate plane and r is the radius of the circle.
Here,
C is the point outside the circle and tangent drawn to the circle from C to B of length 12, the radius of the circle is 5. Since the radius is always perpendicular to the circle's tangent,
So
ABC is right angle triangle
AB = 5 ; BC = 12
Now applying the Pythagorean theorem
AC² = AB² + BC²
AC = √(5² + 12²)
Ac = √(25+144)
AC = √169
AC = 13
Now,
AC = AE + EC
(AE = AB)
AC = AB + EC
13 = 5 + EC
EC = 8
Thus, the required length from the point outside the circle to the point on the circle i.e. CE is 8 and the length from the point outside the circle to the center is 13.
Learn more about circle here:
brainly.com/question/11833983
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