Measuring Major and Minor Arcs
An isosceles triangle _ABC_ is circumscribed by a circle of radius 5. Sides _AB_ and _AC_ of the triangle have the same lengths. The minor arc length of _AB_ is twice the minor arc length of _BC_.
What is the minor arc length of _AC_?
Correct.
Triangle _ABC_ is isosceles, and two of the arcs on the circumcircle will have the same lengths. Since sides _AB_ and _AC_ have the same lengths, the arcs will have the same lengths:
Arc _AB_ is twice _BC_, so arc _AC_ is twice _BC_. These arcs will add to the circumference of the circle, _C_:
$$\displaystyle C= AB + BC + AC=2BC + BC + 2BC=5BC$$
You can calculate the circumference with the given radius:
$$\displaystyle C=2\pi r=2\pi\times5=10\pi$$
$$\displaystyle 5BC=10\pi $$
$$\displaystyle BC=2\pi $$
$$\displaystyle AC=2BC=2(2\pi )$$
$$\displaystyle AC=4\pi $$
Incorrect.
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The arc lengths of _AC_ and _AB_ are both twice the length of _BC_.
Incorrect.
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Double check what value you are reporting. Make sure that you are calculating the length of _AC_, not _BC_.
Incorrect.
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Double check your calculations.
Incorrect.
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This choice is just a distractor with the radius, 5, multiplied by $$\pi $$.
$$\pi$$
$$2\pi$$
$$3\pi$$
$$4\pi$$
$$5\pi$$
