Unit 29: Practical Geometry - Circles - Explanation Of Transverse Common Tangent Or Internal Tangent Of Two Unequal Circles - Mathematics II - For Class X (Science Group)

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Mathematics II
For Class X (Science Group)
Unit 29: Practical Geometry

By Sir Wasim Ahmad
(ICS Digital Virtual Coaching)

• Definition
• Video Tutorial
• Example

Transverse Common Tangent Or Internal Tangent Of Two Unequal Circles

Definition:

A common tangent is called transverse common tangent or internal tangent to two circles if it intersects the line segment joining the centres of the two given circles.

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Video Tutorial:

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Example:

Example: Draw the transverse common tangents to two circles with centres A and B, also having radii 3.1cm and 1.9cm such that the distance between their centres is 7.6cm
Given: Two circles with centres A and B having radii 3.1cm and 1.9cm respectively and m AB =7.6cm

Required: To draw tranverse common tangents to two given circles.

Steps of Construction:

1. Draw AB of 7.6cm
2. With centers A and B, draw two circles of radii 3.1cm and 1.9 cm respectively.
3. Bisect AB at point O and draw a circle of radius equal to m OA with centre O.
4. With centre A (centre of bigger circle) and radius of 5 cm (i.e. 3.1cm + 1.9cm = 5cm) draw a circle which cuts the previous circle at points P and Q.
5. Draw AP which cuts the given larger circle at point S.
6. Draw AQ which cuts the given larger circle at point L.
7. Draw BM || AQ and BT || AP.
8. Draw ST and LM.

Now ST and LM are the required transverse common tangents.

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