An arc has the same measure as its central angle, and the whole way round is 360. For chords, the perpendicular from the center cuts the chord in half, which makes a right triangle you already know how to solve.
A chord of length 24 is 5 from the center. Find the radius
Half the chord is 12.
12, 5 and the radius make a right triangle.
12 squared plus 5 squared is 169.
The answer is 13.
Where students go wrong
Using the whole chord in the right triangle. The perpendicular from the center bisects it, so only half the chord is a leg. Using all 24 gives a radius far too large.
Also called central angles, major and minor arcs or chord length.
What you can put on this worksheet
Arc measures and central angles
Two adjacent arcs measure 84∘ and 193∘. Find the remaining arc→ 83∘
Chords, distance from the center, radius
A chord is 24 from the center of a circle of radius 26. Find its length→ 20
Questions about these worksheets
Yes. Every arcs and chords sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the arcs and chords questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 2: arc measures and central angles and chords, distance from the center, radius. Tick as many as you want and set how many of each, or let it spread them evenly.
Using the whole chord in the right triangle. The perpendicular from the center bisects it, so only half the chord is a leg. Using all 24 gives a radius far too large.