Answer:
AB = 32
Explanation:
Given:
AD = 40
CD = 9
Required:
Find the length of segment AB
Solution:
BC and CD are radius of the circle. Therefore,
BC = CD = 9
AB = AC - BC
AB = AC - 9
We need to find AC
Since AD is tangent, CD is perpendicular to AD, this means that <D is a right angle. This makes ∆ADC a right triangle.
Therefore, we can apply Pythagorean theorem to find AC.
Thus:
AC² = AD² + CD²
AC² = 40² + 9²
AC² = 1,681
AC = √1,681
AC = 41
Let's find BC:
AB = AC - 9
Plug in the value of AC
AB = 41 - 9
AB = 32