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)