In the figure given below, AD and BC are equal and perpendicular to the same l

Question

In the figure given below, AD and BC are equal and perpendicular to the same line segment AB. CD cuts AB at O. Then the relation between OC and OD is _____ .

Options:

A . OD = 12 OC

B . OD = OC

C . OD > OC

D . OD < OC

Answer: Option B
:
B
Consider

Δ B O C

and

Δ A O D

1)AD = BC ( Given )
2)

∠ C B O = ∠ D A O

= 90°
3)

∠ B O C = ∠ A O D

......(vertically opposite angles)

∴ Δ B O C ≅ Δ A O D

....[AAS Criterion]

\Rightarrow

OC = OD ....(congruent parts of congruent triangle)

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