JEE MATHEMATICS MCQ: PROPERTIES OF TRIANGLES

1 Easy

1 of 1

Application +4 | -1

The value of

\frac{1}{{r_1^2}} + \frac{1}{{r_2^2}} + \frac{1}{{r_3^2}} + \frac{1}{{{r^2}}}

View answer and explanation

Correct option: B

\frac{{{a^2} + {b^2} + {c^2}}}{{{\Delta ^2}}}

Option B (

\frac{{{a^2} + {b^2} + {c^2}}}{{{\Delta ^2}}}

) is correct because by substituting the formulas for

r

r_1

r_2

, and

r_3

in terms of area and semi-perimeter, and simplifying, we arrive at the given expression.

More Questions from PROPERTIES OF TRIANGLES

Practice All Chapter MCQs →

{p_1},{p_2},{p_3}

\Delta \;ABC

A,B,C

\Delta

p_1^{ - 2} + p_2^{ - 2} + p_3^{ - 2}

5k,\;6k,\;5k

k

\Delta \,ABC

a = \left( {b - c} \right)\sec \theta

\frac{{2\,\sqrt {bc} }}{{b - c}}\,\,\sin \,\,\frac{A}{2} =

\Delta \;ABC,\frac{{b + c}}{a}

\Delta = {a^2} - {\left( {b - c} \right)^2}

\Delta

\Delta \;ABC

\tan A

A

2 s