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Question

In the given figure, AB, CD are two chords, FG is diameter, OB=OC and AO+OC=10cm, then (OD+OB)
is equal to

A

20 cm
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B

10 cm
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C

30 cm
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D

35 cm
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Solution

The correct option is B
10 cm
Given that AO + OC = 10 cm and OB = OC.

In ΔODB and ΔOAC,OB=OC (Given)ODB=OAC(Angles subtended by chord BC in same segment are equal)



AOC=DOB(Vertically opposite angles)

ΔODBΔOAC (By AAS congruence rule)

OD=OA (By CPCT)

Thus, OD+OB=OA+OC=10 cm.

Hence, the correct answer is option (b).

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