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

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Srutarshi Tripathi · Answer

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 · Answer

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

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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

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

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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

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

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