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# ABC is a given triangle. Forces P,Q,R acting along the lines OA,CB,OC are in equilibrium. Show that P:Q:R=a^2(b^2+c^2-a^2):b^2(c^2+a^2-b^2):c^2(a^2+b^2-c^2) if O is the circumcentre of the triangle

Srutarshi Tripathi
38 Points
9 months ago
By Lami‟s theorem, P/sin(BOC) = Q/sin(COA) = R/sin(AOB)OR, P/sin(2A) = Q/sin(2B) = R/sin(2C)Or, P/2sinA.cosA = Q/2sinB.cosB = R/2sinC.cosC ………………………….(1)WE HAVE, cos A = (b^2 + c^2 – a^2)/2bcsinA = 2.(area)/bcso, 2sinAcosA = 2(2.(area)/bc).( (b^2 + c^2 – a^2)/2bc) =2.(area)( b^2 + c^2 – a^2)/b^2 .c^2Similarly we find 2sinB.cosB and 2sinC.cosC and putting these values in (1) and dividing it by a^2.b^2.c^2, we get the required result
Siva
13 Points
3 months ago
A body is at rest on a rough inclined plane of inclination 𝛼 to the horizon, being acted on
by a force making an angle 𝜃 with the plane. Find the limit between which the force
must lie and also find the magnitude and direction of the least force required to drag the
body up the inclined plane