Tangent to a Circle Math Example 1

Solution

1. 1
   Step 1: Recall that a tangent to a circle is perpendicular to the radius at the point of tangency. So $OP \perp AP$, making triangle $OAP$ a right triangle with the right angle at $P$.
2. 2
   Step 2: Identify the hypotenuse: $OA = 25$ cm (from center to external point), and one leg $OP = 7$ cm (radius).
3. 3
   Step 3: Apply the Pythagorean theorem: $AP^2 + OP^2 = OA^2$, so $AP^2 = 25^2 - 7^2 = 625 - 49 = 576$.
4. 4
   Step 4: Take the square root: $AP = \sqrt{576} = 24$ cm.