CATGeometry > Mediumabr2a2+b2\frac{abr^2}{a^2+b^2}a2+b2abr2abr22(a2+b2)\frac{abr^2}{2(a^2+b^2)}2(a2+b2)abr22abr2a2+b2\frac{2abr^2}{a^2+b^2}a2+b22abr24abr2a2+b2\frac{4abr^2}{a^2+b^2}a2+b24abr2✅ Correct Option: 3Related questions:CAT 2022 Slot 2The length of each side of an equilateral triangle ABC is 3 cm3 \mathrm{~cm}3 cm. Let D be a point on BC such that the area of triangle ADC is half the area of triangle ABDA B DABD. Then the length of ADA DAD, in cm , isCAT 2018 Slot 1In a circle with center OOO and radius 1 cm1 \mathrm{~cm}1 cm, an arc ABA BAB makes an angle 606060 degrees at OOO. Let RRR be the region bounded by the radii OA,OB\mathrm{OA}, \mathrm{OB}OA,OB and the arc ABABAB . If CCC and DDD are two points on OAOAOA and OBOBOB , respectively, such that OC=OD\mathrm{OC}=\mathrm{OD}OC=OD and the area of triangle OCDOCDOCD is half that of RRR , then the length of OCOCOC , in cm , isCAT 2022 Slot 2In triangle ABC, altitudes AD and BE are drawn to the corresponding bases. If ∠BAC=45∘\angle BAC = 45^\circ∠BAC=45∘ and ∠ABC=θ\angle ABC = \theta∠ABC=θ, then ADBE\frac{AD}{BE}BEAD equals