Question

the centre of two circles of radii 5cm and 3cm and and 9CM apart. draw a pair of tangents from the centre of a circle to another circle

Answer 1

Thank you for asking this question. Here is your answer:

radius of circle A = 5 cm,  

radius of circle B = 3cm,  

distance between the centers of the two circles = 9 cm.

Let  O ₁  and  O ₂  be the center of Circle A and Circle B.

Length of common tangent  X Y

Construct line segment  Z O ₂

Which is parallel to  X Y

Now we will use the Pythagorean theorem, we know that

Z O ₂  =  √ O ₁O²₂  −  O ₁ Z ²

= √ 13 ² - 2²

= √ 165

=  12.85

Hence, length of common tangent  

X Y  =  Z O ₂

= √ 165

=  12.85  (2dp)

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