INTERNAL AND EXTERNAL TANGENTS OF A CIRCLE

Lines are internal tangents, if they intersect the segment joining the centers of two circles

External tangents are lines that do not cross the segment joining the centers of the circles.

Tell whether the common tangent(s) are internal or external.

Question 1 :

Solution :

When we draw segments from the center of the circle, it does not intersect the tangents. So, they are external tangents.

Question 2 :

Solution :

When we draw segments from the center of the circle, it intersects the tangents. So, it is internal tangent.

Question 3 :

Solution :

When we draw segments from the center of the circle, it intersects the tangents. So, they are internal tangents.

Copy the diagram. Tell how many common tangents the circles have. Then sketch the tangents.

Question 1 :

Solution :

We can draw 2 internal tangents and 2 external tangents.

Question 2 :

Solution :

We cannot draw any common tangents for the given circles.

Question 3 :

Solution :

We can two common tangents for the circles given above and they are external tangents.

Are these lines internally or externally tangent? Connect the centers and apply the definitions. Are the circles tangent internally or externally?

Question 1 :

Solution :

(i)  The line segment joining the centers is intersecting the the common tangent. So, it is internal tangent.

(ii)  The line segment joining the centers is not intersecting the the common tangent. So, it is external tangent.

Question 2 :

In the diagram P and Q are tangent circles. RS is a common tangent. Find RS.

Solution :

RS is a external tangent.

Tangents are perpendicular to the radius  at the point of tangency.

<QRS  =  <PSR  =  90 degree

We can connect a point on RQ from P. So, it will create the rectangle PSRT.

In triangle TPQ,

QP =  TQ2 + TP2

82  =  22 + TP2

64-4  =  TP2

TP  =  60

TP  =  2√15

RS  =  2√15

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