Question

In the figure shown, the triangle is inscribed in the semicircle. If the length of line segment AB is 8 and the length of line segment BC is 6, what is the length of arc ABC?

• A. $15\pi$
• B. $12\pi$
• C. $10\pi$
• D. $7\pi$
• E. $5\pi$

Answer 1

Answer: (E)

$5\pi$

AC is the diameter of he circle.

So, diameter AC extends a right angle on the circle.

So, measure of angle ABC is ${90}^o$.

So, in right $△$ ABC, AB${}^2$ + BC${}^2$ = AC${}^2$

Therefore, AC${}^2$ = $8^2+6^2$ = ${10}^2$

So, AC = 10 units.

AC is the diameter = 2 $\times$ the radius.

So, radius of given circle is 5 units.

Length of arc ABC = length of the semicircle = $\pi$ R = 5$\pi$

(option E)