b Recall that if two segments from the same exterior point are tangent to a circle they are congruent.
A
a ≈ 37.95 inches
B
b ≈ 37.95 inches
Practice makes perfect
a We are given that in the drawn arbor AC and BC are tangents to ∘ D. We also know that the radius of the circle is 26 inches and EC= 20 inches. Let's take a look at the given diagram.
As we can see, △ ADC is a right triangle. Therefore we can find AC using the Pythagorean Theorem. According to this theorem the sum of the squared legs of a right triangle is equal to its squared hypotenuse.
AD^2+AC^2=DC^2
Let's solve the above equation by substituting the appropriate segment lengths. Notice that DC= 26+ 20=46 inches. Also, since AC represents a length we will consider only the positive case when taking the square root of AC^2.
b In this part we are asked to find BC. Let's look at the diagram.
Remember that if two segments from the same exterior point are tangent to a circle, then they are congruent. This means that AC=BC. Since we found in the previous part that AC is approximately 37.95 inches, BC is also 37.95 inches.
