Question

angle bcd is a circumscribed angle of circle a. what is the length of line segment ac? 10 units 12 units 14 units 16 units

Explanation:

Step1: Recall tangent - radius property

Since $\angle BCD$ is a circumscribed angle of circle $A$ and $AB$ and $AD$ are radii and $BC$ and $CD$ are tangents, $\angle ABC=\angle ADC = 90^{\circ}$, and $AB = AD$ (radii of the same circle), and $BC=CD$ (tangents from an external point to a circle are equal). Triangle $ABC$ is a right - triangle with $AB = 8$ and $BC = 6$.

Step2: Apply the Pythagorean theorem

In right - triangle $ABC$, by the Pythagorean theorem $AC^{2}=AB^{2}+BC^{2}$. Substitute $AB = 8$ and $BC = 6$ into the formula: $AC=\sqrt{8^{2}+6^{2}}=\sqrt{64 + 36}=\sqrt{100}$.

Step3: Calculate the value of $AC$

$\sqrt{100}=10$.

Answer:

10 units