Question : If C1 and C2 are the centres of two circles and r1 and r2 are the respective radii such that the distance between the centres is equal to the sum of the radii of the two circles, find the number of common tangents.
Option 1: 4
Option 2: 2
Option 3: 1
Option 4: 3
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Correct Answer: 3
Solution : Since the distance between the centres is equal to the sum of the radii of the two circles, the two circles touch each other as shown in the figure. So, there are 3 common tangents. Hence, the correct answer is 3.
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Question : Find the number of common tangents, if $r_1+r_2=c_1 c_2$. (With usual notations, $r_1\ \text{and}\ r_2$ and $\mathrm{C}_1 \ \text{and}\ \mathrm{C}_2$ are the radii and centres of the two circles.)
Question : The diameters of the two circles are 12 cm and 20 cm, respectively and the distance between their centres is 16 cm. Find the number of common tangents to the circles.
Question : Two circles of radius 10 cm and 5 cm touch each other externally at point A. PQ is the direct common tangent of those two circles of centres O1 and O2, respectively. The length of PQ is equal to:
Question : The distance between the centres of two circles having radii 16 cm and 8 cm, is 26 cm. The length (in cm) of the direct common tangent of the two circles is:
Question : The distance between the centres of two circles is 61 cm and their radii are 35 cm and 24 cm. What is the length (in cm) of the direct common tangent to the circles?
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