All three rules here are the same rule. From any point, the two pieces along one line multiply to the two pieces along the other. Inside the circle that is the two bits of each chord; outside it is the near piece times the whole secant, and a tangent counts as both, so it gets squared.
A tangent and a secant are drawn from the same outside point. The secant's near piece is 7 and the whole secant is 28. Find the tangent
Two secants are drawn from the same outside point. On the first, the near piece is 5 and the whole secant is 8. On the second the near piece is 4. Find the whole second secant
Find x
A tangent and a secant are drawn from the same outside point. The secant's near piece is 1 and the whole secant is 100. Find the tangent
Two secants are drawn from the same outside point. On the first, the near piece is 4 and the whole secant is 6. On the second the near piece is 2. Find the whole second secant
Find x
A tangent and a secant are drawn from the same outside point. The secant's near piece is 1 and the whole secant is 49. Find the tangent
Two secants are drawn from the same outside point. On the first, the near piece is 6 and the whole secant is 8. On the second the near piece is 3. Find the whole second secant
Find x
A tangent and a secant are drawn from the same outside point. The secant's near piece is 5 and the whole secant is 20. Find the tangent
Two secants are drawn from the same outside point. On the first, the near piece is 8 and the whole secant is 9. On the second the near piece is 4. Find the whole second secant
Find x
A tangent and a secant are drawn from the same outside point. The secant's near piece is 1 and the whole secant is 81. Find the tangent
Two secants are drawn from the same outside point. On the first, the near piece is 3 and the whole secant is 8. On the second the near piece is 4. Find the whole second secant
Find x
A tangent and a secant are drawn from the same outside point. The secant's near piece is 4 and the whole secant is 16. Find the tangent
Two secants are drawn from the same outside point. On the first, the near piece is 6 and the whole secant is 9. On the second the near piece is 3. Find the whole second secant
Find x
A tangent and a secant are drawn from the same outside point. The secant's near piece is 9 and the whole secant is 16. Find the tangent
A tangent and a secant are drawn from the same outside point. The secant's near piece is 7 and the whole secant is 28. Find the tangent14
Two secants are drawn from the same outside point. On the first, the near piece is 5 and the whole secant is 8. On the second the near piece is 4. Find the whole second secant10
Find x9
A tangent and a secant are drawn from the same outside point. The secant's near piece is 1 and the whole secant is 100. Find the tangent10
Two secants are drawn from the same outside point. On the first, the near piece is 4 and the whole secant is 6. On the second the near piece is 2. Find the whole second secant12
Find x15
A tangent and a secant are drawn from the same outside point. The secant's near piece is 1 and the whole secant is 49. Find the tangent7
Two secants are drawn from the same outside point. On the first, the near piece is 6 and the whole secant is 8. On the second the near piece is 3. Find the whole second secant16
Find x2
A tangent and a secant are drawn from the same outside point. The secant's near piece is 5 and the whole secant is 20. Find the tangent10
Two secants are drawn from the same outside point. On the first, the near piece is 8 and the whole secant is 9. On the second the near piece is 4. Find the whole second secant18
Find x6
A tangent and a secant are drawn from the same outside point. The secant's near piece is 1 and the whole secant is 81. Find the tangent9
Two secants are drawn from the same outside point. On the first, the near piece is 3 and the whole secant is 8. On the second the near piece is 4. Find the whole second secant6
Find x4
A tangent and a secant are drawn from the same outside point. The secant's near piece is 4 and the whole secant is 16. Find the tangent8
Two secants are drawn from the same outside point. On the first, the near piece is 6 and the whole secant is 9. On the second the near piece is 3. Find the whole second secant18
Find x3
A tangent and a secant are drawn from the same outside point. The secant's near piece is 9 and the whole secant is 16. Find the tangent12
Two chords cross inside a circle. One is cut into 4 and 9; the other into 6 and x. Find x
The pieces of one chord multiply to the pieces of the other.
4 times 9 is 36.
36 divided by 6 is 6.
The answer is 6.
Where students go wrong
Using the outside piece of a secant twice, or the whole secant twice. It is near piece times whole secant, and the whole one includes the near piece. Only a tangent is multiplied by itself.
Also called power of a point, intersecting chords theorem or tangent secant theorem.
What you can put on this worksheet
Two chords crossing inside
Find x→ 3
A tangent and a secant
A tangent and a secant are drawn from the same outside point. The secant's near piece is 1 and the whole secant is 49. Find the tangent→ 7
Two secants
Two secants are drawn from the same outside point. On the first, the near piece is 3 and the whole secant is 6. On the second the near piece is 2. Find the whole second secant→ 9
A chord, its distance from the center, and the radius
A chord sits 48 from the center of a circle of radius 52. Find the length of the chord→ 40
Questions about these worksheets
Yes. Every segment lengths in circles 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 segment lengths in circles 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 two 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 4: two chords crossing inside, a tangent and a secant, two secants and a chord, its distance from the center, and the radius. Tick as many as you want and set how many of each, or let it spread them evenly.
Using the outside piece of a secant twice, or the whole secant twice. It is near piece times whole secant, and the whole one includes the near piece. Only a tangent is multiplied by itself.