Question

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

• A.
  20 cm
• B.
  10 cm
• C.
  30 cm
• D.
  35 cm

Answer 1

The correct option is B

10 cm
Given that AO + OC = 10 cm and OB = OC.

In $\Delta ODBand\Delta OAC,OB=OC\left(Given\right)\angle ODB=\angle OAC$(Angles subtended by chord BC in same segment are equal)



$\angle AOC=\angle DOB$(Vertically opposite angles)

$\therefore \Delta ODB\cong \Delta OAC$ (By AAS congruence rule)

$\Rightarrow OD=OA\left(ByCPCT\right)$

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

Hence, the correct answer is option (b).