Q66.Let the tangent to the circle x2 + y2 = 25 at the point R(3, 4) meet x -axis and y-axis at point P and Q , respectively. If r is the radius of the circle passing through the origin O and having centre at the incentre of the triangle OPQ, then r2 is equal to (1) 529 (2) 125 64 72 (3) 625 (4) 585 72 66
What This Question Tests
This problem involves finding the equation of a tangent to a circle, then determining the intercepts to form a triangle, and finally calculating the incentre and radius of a circle centered at the incentre passing through the origin.
Concepts Tested
Formulas Used
Tangent to x^2+y^2=r^2 at (x1,y1): x x1 + y y1 = r^2
Incentre coordinates: I = (ax1+bx2+cx3)/(a+b+c), ...
Distance formula
📚 NCERT Sections This Tests
9.17 — (A) Sin I¢C = 1.44/1.68 Which Gives I¢C = 59°. Total Internal Reflection
Physics Class 12 · Chapter 9
9.17 (a) sin i¢c = 1.44/1.68 which gives i¢c = 59°. Total internal reflection takes place when i > 59° or when r < rmax = 31°. Now, (sin i /sin r max max ) = 1.68 , which gives imax ~ 60°. Thus, all incident rays of angles in the range 0 < i < 60° will suffer total internal reflections in the pipe. (If the length of the pipe is finite, which it is in practice, there will be a lower limit on i determined by the ratio of the diameter to the length of the pipe.) (b) If there is no outer coating, i¢c = sin–1(1/1.68) = 36.5°. Now, i = 90° will have r = 36.5° and i¢ = 53.5° which is greater than i¢c. Thus, all incident rays (in the range 53.5° < i < 90°) will suffer total internal reflections.
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
12.7 — The Radius Of The Innermost Electron Orbit Of A Hydrogen Atom Is
Physics Class 12 · Chapter 12
12.7 The radius of the innermost electron orbit of a hydrogen atom is 5.3×10–11 m. What are the radii of the n = 2 and n =3 orbits?
📋 Question Details
- Chapter
- Coordinate Geometry
- Topic
- Tangents to a circle & incentre of a triangle
- Year
- 2021
- Shift
- 17 Mar Shift 2
- Q Number
- Q66
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 10: Straight Lines, Class 11 Mathematics Ch 11: Conic Sections
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