Question

Construct a rectangle ABCD of lengh $6$cm and breadth $4$ cm. Construct angle bisectors of $\angle A$ and $\angle B$. Let them meet at O.The distance of O from length AB is:

• A. $3$
• B. $10$
• C. $2$
• D. $8$

Answer 1

The correct option is A $3$

It is given that AO is angle bisector of angle A and BO is angle bisector of angle B so angle OAP = angle OBP = 45 degrees.

We have OP perpendicular to AB so angle OPB = 90 degrees..

In triangle OPB

angle OBP = 45 degree , angle OPB = 90 degree so angle POB =45 degree.

Two angles of the triangle are equal so the triangle is the isosceles triangle.

OP = PB

Similarly for triangle AOP

OP = AP

Wet OP =AP =PB

OP=AP = $\frac{AB}{2}$

It is not given that AB is length or breadth

OP = AP = 2 or 3

Distance of point O from AB is OP so our answer should be option A and C