In the adjoining figure, ABCD is a quadrilateral in which BN and DM are drawn perpendiculars to AC such that BN = DM. If OB = 4 cm, then BD is

1. 6 cm

2. 8 cm

3. 10 cm

4. 12 cm

∠MOD = ∠NOB (Vertically opposite angles)

∠DMO = ∠BNO (Each = 90°)

BN = DM (Given)

Hence, △MOD ≅ △NOB by AAS axiom.

We know that corresponding parts of congruent triangles are equal.

OD = OB = 4 cm.

BD = OB + OD = 4 + 4 = 8 cm.

Hence, Option 2 is the correct option.