Question

State that whether given statement is true or false

The sides AB and AC of $\Delta ABC$ are produce to D and E respectively and the bisectors of $\angle CBD$ and $\angle BCD$ meet at $O$ if $AB>AC$, prove that $OC>OB$

• A. True
• B. False

Answer 1

The correct option is A True

In $\Delta ABC$

If $AB>AC$ then

$\angle ACB>\angle ABC$

Now at point B

$\angle ABC+2\angle CBO={180}^{\circ }$ (Linear pair)

$\angle CBO={90}^{\circ }-\frac{\angle ABC}{2}$ _____ $\left(1\right)$

Now at point C

$\angle ACB+2\angle BCO={180}^{\circ }$ (Linear pair)

$\angle BCO={90}^{\circ }-\frac{\angle ACB}{2}$ _______ $\left(2\right)$

From $\left(1\right)$ & $\left(2\right)$ $\to$ If $\angle ACB>\angle ABC$ then $\angle CBO>\angle BCO$

Now in $\Delta OBC$

If $\angle CBO>\angle BCO$ then $OC>OB$