Question

O is a point inside a rhombus ABCD such that BO = CO. Prove that the points O, A and C
are collinear.

Answer 1

Answer:

BO = DO Then, O,A and C are collinear.

Step-by-step explanation:

Consider a rhombus ABCD and O is the interior point in the rhombus.

Now, it is given that OB = OD,

⇒ O is the center.

Hence, BD and AC are the diagonals.

Since, we know that diagonals of a rhombus are perpendicular bisectors of each other.

Therefore, ∠AOB = 90° ∠AOD = 90°

∠BOC = 90° ∠COD = 90°

NOW, ∠AOB +∠BOC = 90°+90°

                                   = 180°

Hence, by linear property.

AOC forms a straight line.

A,O,C are collinear