IPMAT Indore 2024Geometry > Hardk2sinθ2+ksinθc2+k2sin2θ\dfrac{k^2 \sin \theta}{2} + k \sin \theta \sqrt{c^2 + k^2 \sin^2 \theta}2k2sinθ+ksinθc2+k2sin2θk2sin2θ2+ksinθc2−k2sin2θ\dfrac{k^2 \sin 2\theta}{2} + k \sin \theta \sqrt{c^2 - k^2 \sin^2 \theta}2k2sin2θ+ksinθc2−k2sin2θk2cos2θ2+ksinθc2−k2sin2θ\dfrac{k^2 \cos 2\theta}{2} + k \sin \theta \sqrt{c^2 - k^2 \sin^2 \theta}2k2cos2θ+ksinθc2−k2sin2θk2cosθ2+ksinθc2+k2sin2θ\dfrac{k^2 \cos \theta}{2} + k \sin \theta \sqrt{c^2 + k^2 \sin^2 \theta}2k2cosθ+ksinθc2+k2sin2θ✅ Correct Option: 2Related questions:Consider a triangle with side lengths 4 meters, 6 meters, and 9 meters. A dog runs around the triangle in such a way that the shortest distance of the dog from the triangle is exactly 1 meter. The total distance covered (in meters) by the dog in one round isLet ABC be an equilateral triangle, with each side of length kkk. If a circle is drawn with diameter AB, then the area of the portion of the triangle lying inside the circle isIn triangle ABC,AB=AC=x,∠ABC=θABC, AB = AC = x, ∠ABC = \thetaABC,AB=AC=x,∠ABC=θ and the circumradius is equal to yyy. Then xy\frac{x}{y}yx equals