Q84.Let ๐ด๐ต be a chord of length 12 of the circle 169 ๐ฅ- 22 + ๐ฆ+ 12 = 4 JEE Main 2022 (29 Jul Shift 2) JEE Main Previous Year Paper If tangents drawn to the circle at points ๐ด and ๐ต intersect at the point ๐, then five times the distance of point ๐ from chord ๐ด๐ต is equal to _____.
What This Question Tests
This problem involves finding the distance of the intersection point of tangents from the chord of contact, requiring knowledge of circle properties, geometry of tangents, and potentially using power of a point or similar geometric relationships.
Concepts Tested
Formulas Used
Equation of circle: (x-h)ยฒ + (y-k)ยฒ = rยฒ
Length of chord formula
Distance from a point to a line
Properties of right-angled triangles formed by radius, tangent, and point P.
๐ NCERT Sections This Tests
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2.4 A spherical conductor of radius 12 cm has a charge of 1.6 ร 10โ7C distributed uniformly on its surface. What is the electric field (a) inside the sphere (b) just outside the sphere (c) at a point 18 cm from the centre of the sphere?
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9.8 A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20cm, and (b) a concave lens of focal length 16cm?
๐ Question Details
- Chapter
- Circles
- Topic
- Tangents from an external point to a circle
- Year
- 2022
- Shift
- 29 Jul Shift 2
- Q Number
- Q84
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections; Class 12 Mathematics Ch 10: Vector Algebra (for distance calculations)
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