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Formula of common tangent to two circles?
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Formula of common tangent to two circles?
Understanding Common Tangents to Two Circles
Common tangents are lines that touch two circles at distinct points without crossing the circles. There are two types of common tangents: external and internal.
Types of Common Tangents
Formula for External Tangents
For two circles with centers (x1, y1) and (x2, y2), and radii r1 and r2 respectively, the formula for the length of the external tangent (L) is:
Where:
Formula for Internal Tangents
For internal tangents, the formula for the length (L) is:
Where:
Conclusion
Understanding these formulas helps in solving geometric problems related to circles, especially in competitive exams like UPSC. Proper application of these formulas can simplify the process of finding tangents and their properties.
Common tangents are lines that touch two circles at distinct points without crossing the circles. There are two types of common tangents: external and internal.
Types of Common Tangents
- External Tangents: These tangents lie outside the two circles and do not intersect the line segment joining the centers of the circles.
- Internal Tangents: These tangents pass between the two circles and intersect the line segment joining their centers.
Formula for External Tangents
For two circles with centers (x1, y1) and (x2, y2), and radii r1 and r2 respectively, the formula for the length of the external tangent (L) is:
- L = sqrt(d^2 - (r1 + r2)^2)
Where:
- d = distance between the centers of the circles
- d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Formula for Internal Tangents
For internal tangents, the formula for the length (L) is:
- L = sqrt(d^2 - (r1 - r2)^2)
Where:
- d = distance between the centers of the circles
- d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Conclusion
Understanding these formulas helps in solving geometric problems related to circles, especially in competitive exams like UPSC. Proper application of these formulas can simplify the process of finding tangents and their properties.
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Formula of common tangent to two circles?
Question Description
Formula of common tangent to two circles? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Formula of common tangent to two circles? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Formula of common tangent to two circles?.
Formula of common tangent to two circles? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Formula of common tangent to two circles? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Formula of common tangent to two circles?.
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