Question

the adjoining figure o is the centre of the circle then find the length of a b

Answer 1

OD =OC RADIUS OF CIRCLE.
NOW OCD BECOMES AN ISOCELS TRANGLE
THEREFORE BASE ANGLES BECOME EQUAL
SINCE ANGLE OCD IS EQUAL TO ANGLE ODC
THEREFORE BOTH ANGLES BECOME 60°
NOW;
IN TRIANGLE OAB AND OCD
ANGLE AOB =ANGLE DOC (given)
ANGLE OBA =ANGLE OCD(angle in the same segment)
therefore triangle AOB is similar to triangle DOC.
since both triangle are similar therefore their angles are equal and both become equilateral triangle.
therefore the length AB is 5 cm.
(the triangles are congruent also as OA ,OB,OC and OD are radii of the same circle.

it is a bit disoriented but hope it helped.

Answer 2

Hope. u like my answer
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Given
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AOD is a straight line

OA , OB ,OC ,OD are the radius of circle

so OA = OB = OC = OD

CD= 5 cm
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Now

∆ AOB and ∆DOC

=> AO = OD { AD is a straight line}

=> angle AOB = angle DOC = 60°

=> OB = OC ( given)

so

∆AOB ≈ ∆DOC

so AB = CD = 5cm

Thus

=> AB = 5 cm

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