Question

- If 'O' is any point inside the rectangle □ABCD such that OB = 2 cm OD = 3 cm and OA=1 cm.
then OC =​

Answer 1

Given,

O is any point inside the rectangle □ABCD.

OB = 2 cm

OD = 3 cm

OA = 1 cm

To find,

The length of OC.

Solution,

We can simply solve this mathematical problem using the following process:

As per geometry;

The opposite sides of a rectangle are parallel and the diagonals form the transversal. And, their alternate angles are equal.

Now,

In ∆AOB and ∆COD;

(I) angle ABO = angle CDO (alternate angles are equal as AB || CD and BD forms the transversal)

II) AB = CD (opposite sides of a rectangle are equal)

III) angle BAO = angle DCO (alternate angles are equal as AB || CD and AC forms the transversal)

=> ∆AOB is congruent to ∆COD {by A-S-A criteria}

=> By CPCT (corresponding parts of congruent triangles), we get;

AO/CO = OB/OD

=> 1 cm / OC = 2 cm / 3 cm

=> OC = 3 cm / 2 cm

=> OC = 1.5 cm

Hence, the length of OC is equal to 1.5 centimeters.