Question

In the given figure, OE = OD. Which of the following are true?

• A. OX is angle bisector $\angle AOB$
• B. C is the midpoint of OX
• C. $\angle AOX=\angle AOB$
• D. $2\angle AOX=\angle AOB$

Answer 1

Answer: (A), (D)

The correct options are
A OX is angle bisector $\angle AOB$
D $2\angle AOX=\angle AOB$

In $△OCD$ and $△OCE$

(i) $OD=OE$ ......(given)

(ii) $\angle CDO=\angle CEO={90}^{\circ }$......(given)

(iii) OC = OC ......(common)

$\therefore △COD\cong △COE$ ....(RHS Postulate)

$\Rightarrow$ $\angle COD=\angle COE$ ...(CPCT)
$\therefore$ OX is angle bisector $\angle AOB$
$\Rightarrow$ $\angle AOX=\angle XOB$

$\angle AOB=\angle AOX+\angle XOB=2\angle AOX$