Question

In the given figure, O is the centre of the circle. OD is a line bisecting AB at C. Which of the following statements are true?

• A. $△$AOC is congruent to $△$BOC
• B. $△$AOC is not congruent to $△$BOC
• C. OA = OD = OB
• D. OC = OB = OA

Answer 1

Answer: (A), (C)

The correct options are
A $△$AOC is congruent to $△$BOC
C OA = OD = OB

Given O is the centre of the circle
$\Rightarrow$ OA, OB and OD are the radii of the circle
$\Rightarrow$ OA = OB = OD

Consider $△$AOC and $△$BOC,

• AO = BO (radii of the same circle)
• OC = OC (common side)
• CA = CB (OD is the bisector of AB)

$\Rightarrow △$AOC $\cong$ $△$BOC ....(by SSS congruence criterion)

$\Rightarrow OA=OD$ (corresponding parts of congruent triangles)