Q66.A circle is inscribed in an equilateral triangle of side of length 12 . If the area and perimeter of any square inscribed in this circle are m and n, respectively, then m + n2 is equal to (1) 408 (2) 414 (3) 396 (4) 312
What This Question Tests
This question involves finding the inradius of an equilateral triangle, which determines the radius of the inscribed circle, and then calculating the area and perimeter of a square inscribed in that circle.
Concepts Tested
Formulas Used
Inradius r = a/(2√3)
Diameter = 2r
Side of inscribed square = d/√2
Area = s²
Perimeter = 4s
📚 NCERT Sections This Tests
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?
2.4 — A Spherical Conductor Of Radius 12 Cm Has A Charge Of 1.6 × 10–7C
Physics Class 11 · Chapter 2
2.4 A spherical conductor of radius 12 cm has a charge of 1.6 × 10–7C 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?
📋 Question Details
- Chapter
- Circles
- Topic
- Circle inscribed in equilateral triangle
- Year
- 2024
- Shift
- 06 Apr Shift 1
- Q Number
- Q66
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
More from this Chapter
Q94.Consider a family of circles which are passing through the point (−1, 1) and are tangent to x− axis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval (1) 0 < k < 1/2 (2) k ≥1/2 (3) −1/2 ≤k ≤1/2 (4) k ≤1/2
Q79.The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y −3 = 0 is (1) (3, −4) (2) (−3, 4) (3) (−3, −4) (4) (3, 4)
Q67.Three distinct points A, B and C are given in the 2 - dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point (−1, 0) is equal to 31 . Then the circumcentre of the triangle ABC is at the point JEE Main 2009 JEE Main Previous Year Paper (1) (0, 0) (2) ( 54 , 0) (3) ( 25 , 0) (4) ( 53 , 0)
Q68.If P and Q are the points of intersection of the circles x2 + y2 + 3x + 7y + 2p −5 = 0 and x2 + y2 + 2x + 2y −p2 = 0, then there is a circle passing through P, Q and (1, 1) for (1) all values of p (2) all except one value of p (3) all except two values of p (4) exactly one value of p