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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
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B
AOC is not congruent to BOC
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C
OA = OD = OB
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D
OC = OB = OA
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Solution

The correct options are
A AOC is congruent to BOC
C OA = OD = OB
Given O is the centre of the circle
OA, OB and OD are the radii of the circle
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)
AOC BOC ....(by SSS congruence criterion)

OA=OD (corresponding parts of congruent triangles)

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