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In the given figure, ABCD is a parallelogram in which AB is extended to E such that $B E = A B$ . Find the relation between OB and BC.

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O B = 23 B C

O B = 13 B C

O B = 12 B C

O B = 25 B C

answer is C.

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Detailed Solution

Given is a parallelogram in which AB is extended to E such that

B E = A B

.
Consider parallelogram ABCD. Question Image

From,

Δ O D C

and

Δ O E B

∠ C O D = ∠ B O E

... (vertically opposite angles)

∠ O C D = ∠ O B E

... (alternate angles with transversal BC)

D C = A B

… (opposite sides of parallelogram)

B E = A B

...(given)
Therefore,

D C = B E

.
Apply the AAS criterion,

Δ O D C ≅ Δ O E B

.
OC = OB ...by CPCT.
Since, BC = OC + OB.
Therefore, ED bisects BC which means O is the midpoint of BC.
Therefore,

O B = 12 B C

.
Hence, option 3 is the correct choice.

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