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The length of common chord of two intersecting circle is 30cm if the diameter of these two circle are 50cm and 34cm then calculate the distance between their centers.?
Verified Answer
The length of common chord of two intersecting circle is 30cm if the d...
Given length of common chord AB = 30 cm
Let the radius of the circle with centre O is OA = 25 cm
Radius of circle with centre P is AP = 17 cm
From the figure,, OP⊥ AB
⇒ AC = CB
∴ AC = 15 cm (Since AB = 30 cm)
In ΔACP, AP^2 = PC^2 + AC^2 [By Pythagoras theorem]
⇒ 17^2 = PC^2 + 15^2
⇒ PC^2 = 289 – 225 = 64
⇒ PC = 8 cm
Consider ΔACO
AO^2 = OC^2 + AC^2 [By Pythagoras theorem]
⇒ 25^2 = OC^2 + 15^2
⇒ OC^2 = 625 – 225 = 400
⇒ OC = 20 cm
From the figure, OP = OC + PC
= 20 + 8 = 28 cm
Hence, the distance between the centres is 28 cm.
This question is part of UPSC exam. View all Class 10 courses
Most Upvoted Answer
The length of common chord of two intersecting circle is 30cm if the d...
The problem involves finding the distance between the centers of two intersecting circles, given the length of their common chord and the diameters of the circles. Let's solve this step by step.
Given:
- Length of common chord = 30 cm
- Diameter of Circle 1 = 50 cm
- Diameter of Circle 2 = 34 cm
Understanding the Problem:
To solve this problem, we need to apply the concept of intersecting chords. When two circles intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. This can be expressed as:
(length of segment of chord 1) * (length of segment of chord 2) = (length of segment of chord 3) * (length of segment of chord 4)
Calculating the Length of the Segments:
In this case, the common chord acts as both chord 1 and chord 2. Let's assume that the common chord divides the circles into segments of lengths x and y.
The length of segment of chord 3 is x, and the length of segment of chord 4 is y. So, we have:
x * y = x * y
This equation implies that the lengths of the segments are equal. Therefore, the length of segment x is equal to the length of segment y.
Calculating the Length of the Segments:
We know that the length of the common chord is 30 cm, and it can be divided into two equal segments, x and y. So,
x + y = 30 cm
Given that x = y, we can rewrite the equation as:
2x = 30 cm
Simplifying further, we find:
x = y = 15 cm
Calculating the Distance between the Centers:
The distance between the centers of the circles is equal to the sum of the radii of the circles. Since the radius is half the diameter, we can calculate the radii as follows:
Radius of Circle 1 = (Diameter of Circle 1) / 2 = 50 cm / 2 = 25 cm
Radius of Circle 2 = (Diameter of Circle 2) / 2 = 34 cm / 2 = 17 cm
The distance between the centers is the sum of the radii:
Distance between Centers = Radius of Circle 1 + Radius of Circle 2 = 25 cm + 17 cm = 42 cm
Conclusion:
The distance between the centers of the two intersecting circles is 42 cm.
Given:
- Length of common chord = 30 cm
- Diameter of Circle 1 = 50 cm
- Diameter of Circle 2 = 34 cm
Understanding the Problem:
To solve this problem, we need to apply the concept of intersecting chords. When two circles intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. This can be expressed as:
(length of segment of chord 1) * (length of segment of chord 2) = (length of segment of chord 3) * (length of segment of chord 4)
Calculating the Length of the Segments:
In this case, the common chord acts as both chord 1 and chord 2. Let's assume that the common chord divides the circles into segments of lengths x and y.
The length of segment of chord 3 is x, and the length of segment of chord 4 is y. So, we have:
x * y = x * y
This equation implies that the lengths of the segments are equal. Therefore, the length of segment x is equal to the length of segment y.
Calculating the Length of the Segments:
We know that the length of the common chord is 30 cm, and it can be divided into two equal segments, x and y. So,
x + y = 30 cm
Given that x = y, we can rewrite the equation as:
2x = 30 cm
Simplifying further, we find:
x = y = 15 cm
Calculating the Distance between the Centers:
The distance between the centers of the circles is equal to the sum of the radii of the circles. Since the radius is half the diameter, we can calculate the radii as follows:
Radius of Circle 1 = (Diameter of Circle 1) / 2 = 50 cm / 2 = 25 cm
Radius of Circle 2 = (Diameter of Circle 2) / 2 = 34 cm / 2 = 17 cm
The distance between the centers is the sum of the radii:
Distance between Centers = Radius of Circle 1 + Radius of Circle 2 = 25 cm + 17 cm = 42 cm
Conclusion:
The distance between the centers of the two intersecting circles is 42 cm.
Community Answer
The length of common chord of two intersecting circle is 30cm if the d...
20cm
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The length of common chord of two intersecting circle is 30cm if the diameter of these two circle are 50cm and 34cm then calculate the distance between their centers.?
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The length of common chord of two intersecting circle is 30cm if the diameter of these two circle are 50cm and 34cm then calculate the distance between their centers.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The length of common chord of two intersecting circle is 30cm if the diameter of these two circle are 50cm and 34cm then calculate the distance between their centers.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of common chord of two intersecting circle is 30cm if the diameter of these two circle are 50cm and 34cm then calculate the distance between their centers.?.
The length of common chord of two intersecting circle is 30cm if the diameter of these two circle are 50cm and 34cm then calculate the distance between their centers.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The length of common chord of two intersecting circle is 30cm if the diameter of these two circle are 50cm and 34cm then calculate the distance between their centers.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of common chord of two intersecting circle is 30cm if the diameter of these two circle are 50cm and 34cm then calculate the distance between their centers.?.
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