Question

BC is tangent to circle P at point C. AB is 12 units long. BC is 5 units long. How long isAP?

Answer 1

First, draw a diagram to visualize the situation:

Since BC is tangent to the circle P, then the angle C is a right angle.

Then, the triangle ACB is a right triangle. From the Pythagorean Theorem, we know that:

`AB^2=AC^2+BC^2`

Since AB and BC are known, isolate the unknown AC from the equation:

`\Rightarrow AC=√(AB^2-BC^2)`

Replace AB=12 and BC=5:

`\Rightarrow AC=√(12^2-5^2)=√(144-25)=√(119)\approx10.9087`

Since P is the center of the circumference and A, C are points in the circumference, then AP=PC. This implies that AC=2AP. Then:

`AP=(1)/(2)AC=(1)/(2)√(119)\approx5.5`

Therefore, the correct choice is option B) 5.5 units.