Question

O is the circumcentre of the triangle ABC and R₁, R₂, R₃ are the radii of the circumcircles of the triangle OBC, OCA and OAB respectively. Then $\frac{a}{R_{1}}$+ $\frac{b}{R_{2}}$+ $\frac{c}{R_{3}}$is equal to-

• A. $\frac{abc}{R}$
• B. $\frac{abc}{R^{3}}$
• C. $\frac{a + b + c}{R}$
• D. $\frac{a^{2} + b^{2} + c^{2}}{R^{2}}$

Answer 1

Answer: (B)

$\frac{abc}{R^{3}}$

Answer 2

We know that R =. Let D₁, D₂ and D₃ represent the

Areas of triangles OBC, OCA

and OAB respectively. Then

R₁= $\frac{a.R.R}{4\Delta_{1}}$

Ž $\frac{a}{R_{1}}$= $\frac{4\Delta_{1}}{R^{2}}$

Similarly, $\frac { \mathrm { b } } { \mathrm { R } _ { 2 } }$ = and $\frac { \mathrm { c } } { \mathrm { R } _ { 3 } }$=

\ $\frac { \mathrm { a } } { \mathrm { R } _ { 1 } }$+ + $\frac { \mathrm { c } } { \mathrm { R } _ { 3 } }$= (D₁+ D₂ + D₃) = =. =