# Construction of transverse common tangent

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The transverse common tangents also meet on the line of centres and divide it internally in the ratio of the radii.

### Objectives

To construct transverse common tangents for the given circles.

### Estimated Time

45 minutes

### Prerequisites/Instructions, prior preparations, if any

- The students should have prior knowledge of a circle , tangent and direct and transverse common tangents .
- They should understand that a tangent is always perpendicular to the radius of the circle.
- They should know construction of a tangent to a given point.
- If the same straight line is a tangent to two or more circles, then it is called a common tangent.
- If the centres of the circles lie on opposite side of the common tangent, then the tangent is called a transverse common tangent.

### Materials/ Resources needed

- Digital: Laptop, geogebra file, projector and a pointer.
- Non Digital: Students' individual construction materials.
- Gegebra file:

### Process (How to do the activity)

Note: In general,

- The two circles are named as C1 and C2
- The distance between the centre of two circles is 'd'
- Radius of one circle is taken as 'R' and other as 'r'
- The length of tangent is 't'

The teacher can explain the step by step construction of Transverse common tangent.

- Developmental Questions (What discussion questions)

- What is a transverse common tangent ?
- What is the radius of the third circle ?
- What is the difference in finding the radius of the third circle in constructing Dct and that of Tct ?
- Why was a third circle constructed ?
- Let us try to construct transverse common tangent without the third circle and see.
- Name the transverse common tangents .
- At what points is the tangent touching the circles ?

- Evaluation (Questions for assessment of the child)

- Is the student able to comprehend the sequence of steps in constructing the tangent.
- Is the student able to identify error areas while constructing ?
- Is the student observing that the angle between the tangent and radius at the point of intersection is 90º ?
- Is the student able to understand the difference in the construction protocol between direct common tangent and transverse common tangent ?

- Question Corner

- What is the formula to find the length of transverse common tangent ?
- Can a direct common tangent be drawn to two circles one inside the other ?
- What are properties of transverse common tangents ?