You visited us 1 times! Enjoying our articles? Unlock Full Access!

Median of Triangle

Consider a tr...

Question

Consider a triangle ABC. $C C_{1}$ and $B B_{1}$ are the medians drawn through angular points B and C respectively and 'G' is the centroid of $Δ$ ABC. If the points A, $C_{1}$ , G and $B_{1}$ are concyclic, then

3 b^{2} = a^{2} + c^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 a^{2} = b^{2} + c^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 c^{2} = a^{2} + b^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D None of these
$c^{2} = b^{2} + a^{2} - 2 a b cos C = b^{2} + a^{2} - 2 a b ⎛ ⎜ ⎜ ⎝ \frac{b}{\frac{a}{2}} ⎞ ⎟ ⎟ ⎠ = b^{2} + a^{2} - {4 b}^{2} ∴ c^{2} = a^{2} - {3 b}^{2} \Rightarrow {3 b}^{2} = a^{2} - c^{2}$

Suggest Corrections

Similar questions

{A A}_{1}, {B B}_{1}, {C C}_{1}

A B C

G

A, C_{1}, G

B

c^{2}, a^{2}, b^{2}

B G . {C C}_{1} = {B C}_{1} . B A

A A_{1^{'}} B B_{1^{'}}

C C_{1}

A_{1}, C_{1^{'}} G

B_{1}

△ = ⎡ ⎢ ⎣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ⎤ ⎥ ⎦

A_{2}, B_{2}, C_{2}

a_{2}, b_{2}, c_{2}

a_{1} A_{2} + b_{1} B_{2} + c_{1} C_{2}

Parallel lines are obtained for the pair of equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ if

Unique point is obtained for the pair of equations $a_{1}$ x + $b_{1}$ y + $c_{1}$ = 0 and $a_{2}$ x + $b_{2}$ y + $c_{2}$ = 0 if __________ .

Join BYJU'S Learning Program