Unit 29: Practical Geometry - Circles - Explanation Of Direct Common Tangent Or External 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
• Method 1: Example

Direct Common Tangent Or External Tangent Of Two Unequal Circles

Definition:

A common tangent is called direct common tangent or external tangent to two circles if it does not intersect the line segment joining the centres of the two given circles.

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Video Tutorial:

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Method 1:

Example: Draw direct common tangents to the given circles of radius 3.4 cm and 2.1cm, where distance between their centres is 7.5 cm.
Given: Two circles with centres A and B having radii 3.4 cm and 2.1 cm respectively such that mAB = 7.5cm

Required: To draw direct common tangents to the given circles.

Steps of Construction:

1. Draw AB of 7.5cm
2. With centres A and B, draw two circles of radii 3.4 cm and 2.1cm respectively.
3. Bisect AB at point O and draw a circle of radius equal to m AO with centre O.
4. With centre A of larger circle, draw a circle of radius 1.3 cm (i.e. 3.4 - 2.1 = 1.3) which cuts the previous circle at points C and D.
5. Draw AC and produce it to intersect the given concentric circle at point Q.
6. Draw AD and produce it to intersect the given concentric circle at point T.
7. Draw BP || AQ and BS || AT by using set squares.
8. Draw PQ and ST.

Now PQ and ST are the required direct common tangents.

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