A tangent touches the circle once and meets the radius there at a right angle, so the radius, the tangent and the segment to the outside point make a right triangle. That is Pythagoras, and it also tests whether a segment is tangent at all. Two tangents drawn from the same outside point are equal.
The angle at T is 90°, so OT, TP and OP are a right triangle.
With OT = 5 and TP = 12, OP is the hypotenuse.
5² + 12² = 169.
The answer is 13.
Where students go wrong
Putting the right angle at the outside point. It is at the point of tangency, so the segment to the centre is the hypotenuse.
Also called tangent lines, tangent and radius, two tangent segments or tangent segment theorem.
What you can put on this worksheet
A tangent meets a radius at a right angle
PTextistangentatText.Findx→ 5
Is the segment tangent
extIsPTexttangenttothecircleatText?→ No
Two tangents from one point
extBothsegmentsfromPextaretangent.Findx→ {6}
Questions about these worksheets
Yes. Every tangents to 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 tangents to 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 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 3: a tangent meets a radius at a right angle, is the segment tangent and two tangents from one point. Tick as many as you want and set how many of each, or let it spread them evenly.
Putting the right angle at the outside point. It is at the point of tangency, so the segment to the centre is the hypotenuse.