Q85.Two circles each of radius 5 units touch each other at the point (1, 2). If the equation of their common tangent is 4x + 3y = 10 , and C1(α, β) and C2(γ, δ), C1 ≠C2 are their centres, then |(α + β)(γ + δ)| is equal to = 1.
What This Question Tests
This question tests the understanding of how to find the centers of two circles given their radius, point of contact, and common tangent. It requires using the property that the radius is perpendicular to the tangent at the point of contact and calculating distances.
Concepts Tested
Formulas Used
Distance of point (x0, y0) from Ax + By + C = 0 is |Ax0 + By0 + C| / sqrt(A^2 + B^2)
Slope of perpendicular lines m1 * m2 = -1
Distance formula between two points
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📋 Question Details
- Chapter
- Circles
- Topic
- Properties of circles and tangents
- Year
- 2021
- Shift
- 27 Aug Shift 2
- Q Number
- Q85
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 10: Straight Lines, Class 11 Mathematics Ch 11: Conic Sections
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