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The circumferences of two circles are touching externally. The distance between their centres is 12 cm. The radius of one circle is 7 cm. Find the diameter (in cm) of the other circle.
- a)12
- b)10
- c)8
- d)5
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The circumferences of two circles are touching externally. The distanc...
When two circles touch each other externally, the distance between their centres is equal to the sum of their radiuses,
⇒ Distance = 12 = 7 + Radius of other circle
⇒ Radius of other circle = 12 – 7 = 5
∴ Diameter of other circle = 2(5) = 10 cm
Most Upvoted Answer
The circumferences of two circles are touching externally. The distanc...
Given:
- The radius of one circle is 7 cm.
- The distance between the centers of the two circles is 12 cm.
- The circumferences of the two circles are touching externally.
We are asked to find the diameter of the other circle.
Let's assume that the radius of the other circle is "r" cm.
Distance between the centers of the circles
- The distance between the centers of the two circles is 12 cm.
Using the Pythagorean theorem, we can find the hypotenuse of the right triangle formed by the centers of the circles and the point where the circumferences touch.
We have:
- The radius of one circle = 7 cm
- The radius of the other circle = r cm
- The distance between the centers of the circles = 12 cm
Using the Pythagorean theorem:
(7 + r)^2 = 12^2
Expanding the equation:
49 + 14r + r^2 = 144
Rearranging the equation:
r^2 + 14r - 95 = 0
Now we can solve this quadratic equation to find the value of "r".
Using the quadratic formula:
r = (-b ± sqrt(b^2 - 4ac)) / 2a
Plugging in the values:
a = 1, b = 14, c = -95
Calculating the discriminant:
D = b^2 - 4ac
D = 14^2 - 4(1)(-95)
D = 196 + 380
D = 576
Since the discriminant (D) is positive, there are two real solutions for "r".
Calculating the values of "r":
r = (-14 ± sqrt(576)) / 2(1)
r = (-14 ± 24) / 2
r = (-14 + 24) / 2 or r = (-14 - 24) / 2
r = 10 / 2 or r = -38 / 2
r = 5 or r = -19
Since the radius cannot be negative, we discard the negative solution.
Therefore, the radius of the other circle is 5 cm.
Diameter of the other circle
The diameter of a circle is twice its radius.
Diameter = 2 * radius
Diameter = 2 * 5 cm
Diameter = 10 cm
Therefore, the diameter of the other circle is 10 cm.
Hence, the correct answer is option B) 10.
- The radius of one circle is 7 cm.
- The distance between the centers of the two circles is 12 cm.
- The circumferences of the two circles are touching externally.
We are asked to find the diameter of the other circle.
Let's assume that the radius of the other circle is "r" cm.
Distance between the centers of the circles
- The distance between the centers of the two circles is 12 cm.
Using the Pythagorean theorem, we can find the hypotenuse of the right triangle formed by the centers of the circles and the point where the circumferences touch.
We have:
- The radius of one circle = 7 cm
- The radius of the other circle = r cm
- The distance between the centers of the circles = 12 cm
Using the Pythagorean theorem:
(7 + r)^2 = 12^2
Expanding the equation:
49 + 14r + r^2 = 144
Rearranging the equation:
r^2 + 14r - 95 = 0
Now we can solve this quadratic equation to find the value of "r".
Using the quadratic formula:
r = (-b ± sqrt(b^2 - 4ac)) / 2a
Plugging in the values:
a = 1, b = 14, c = -95
Calculating the discriminant:
D = b^2 - 4ac
D = 14^2 - 4(1)(-95)
D = 196 + 380
D = 576
Since the discriminant (D) is positive, there are two real solutions for "r".
Calculating the values of "r":
r = (-14 ± sqrt(576)) / 2(1)
r = (-14 ± 24) / 2
r = (-14 + 24) / 2 or r = (-14 - 24) / 2
r = 10 / 2 or r = -38 / 2
r = 5 or r = -19
Since the radius cannot be negative, we discard the negative solution.
Therefore, the radius of the other circle is 5 cm.
Diameter of the other circle
The diameter of a circle is twice its radius.
Diameter = 2 * radius
Diameter = 2 * 5 cm
Diameter = 10 cm
Therefore, the diameter of the other circle is 10 cm.
Hence, the correct answer is option B) 10.
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The circumferences of two circles are touching externally. The distance between their centres is 12 cm. The radius of one circle is 7 cm. Find the diameter (in cm) of the other circle.a)12b)10c)8d)5Correct answer is option 'B'. Can you explain this answer?
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