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JEE MATHEMATICS MCQ: PROPERTIES OF TRIANGLES

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If in a △ABC,a2+b2+c2=8R2\triangle A B C, a^2+b^2+c^2=8 R^2, where R=R= circumradius, the the triangle is
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Correct option: C
right angled
Option C (right angled) is correct because the given condition a2+b2+c2=8R2a^2 + b^2 + c^2 = 8R^2 implies that sin⁡2A+sin⁡2B+sin⁡2C=2\sin^2 A + \sin^2 B + \sin^2 C = 2, which leads to one of the angles being π2\frac{{\pi}}{{2}}.

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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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