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JEE MATHEMATICS MCQ: PROPERTIES OF TRIANGLES

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In a Δ ABC\Delta \,ABC,

sin⁡A+sin⁡B+sin⁡C=1+2and,  cos⁡A+cos⁡B+cos⁡C=2\begin{array}{l} \sin A + \sin B + \sin C = 1 + \sqrt 2 \\ \mathrm{and},\mathrm{\;}\cos A + \cos B + \cos C = \sqrt 2 \end{array}

if, the triangle is
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Correct option: D
Right angled isosceles
Option D (Right angled isosceles) is correct because it is the only type of triangle where the given conditions sin⁡A+sin⁡B+sin⁡C=1+2\sin A + \sin B + \sin C = 1 + \sqrt 2 and cos⁡A+cos⁡B+cos⁡C=2\cos A + \cos B + \cos C = \sqrt 2 hold true.

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If p1,p2,p3{p_1},{p_2},{p_3} are altitudes of a Δ  ABC\Delta \;ABC drawn from the vertices A,B,CA,B,C and Δ\Delta the area of the triangle, then p1−2+p2−2+p3−2p_1^{ - 2} + p_2^{ - 2} + p_3^{ - 2} is equal to If the sides of the triangles are 5k,  6k,  5k5k,\;6k,\;5k and radius of incircle is 6, the value of kk is equal to In a Δ ABC\Delta \,ABC, if a=(b−c)sec⁡θa = \left( {b - c} \right)\sec \theta, then 2 bcb−c  sin⁡  A2=\frac{{2\,\sqrt {bc} }}{{b - c}}\,\,\sin \,\,\frac{A}{2} = In Δ  ABC,b+ca\Delta \;ABC,\frac{{b + c}}{a} is equal to If Δ=a2−(b−c)2\Delta = {a^2} - {\left( {b - c} \right)^2}, where Δ\Delta is the area of Δ  ABC\Delta \;ABC, then tan⁡A\tan A is equal to If AA is the area and 2s2 s is the sum of the sides of a triangle, then
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