In brief, one should know that three circles touch each other externally at three non co-linear points. Hence it is not possible to draw a line i.e. common tangent passing through three non co-linear points of contact of three externally touching circles.
What are three tangents?
Three tangents to a circle. Question: The three lines PS, PT, and RQ are tangents to the circle. The points S, X, and T are the three points of tangency.
How many common tangents do the three circles have?
Lesson Summary
| Position | Number of Common Tangents |
|---|---|
| Touching externally | 3 |
| Intersecting at two points | 2 |
| Touching internally | 1 |
| One lying inside other | 0 |
How many common tangents are there?
There can be four common tangents to two circles. The tangents can be either direct or transverse. When the two circles neither intersect nor touch each other, there are four common tangents.
How do you find the radius of a 3 tangent circle?
According to WolframAlpha’s page on tangent circles, the radius of c3 can be calculated using the following formula r3=r1×r2(√r1+√r2)2, which can be simplified to 1√r3=1√r1+1√r2.
How do you construct a tangent?
Point to Tangents on a Circle
- Draw a line connecting the point to the center of the circle.
- Construct the perpendicular bisector of that line.
- Place the compass on the midpoint, adjust its length to reach the end point, and draw an arc across the circle.
- Where the arc crosses the circle will be the tangent points.
Whats a no common tangent?
No Common Tangent: If one circle line completely inside another circle without cutting or touching it at any point then the circles will have no common tangent. Three Common Tangents: If two circles touch each other externally at one point, they will have three common tangents.
