Multiple choice

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:

  1. $3$
  2. $10$
  3. $2$
  4. $8$
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A Correct answer
Explanation

In a rectangle ABCD, the angle bisectors of A and B meet at point O inside the rectangle. Since angle A and angle B are 90 degrees, the bisectors meet at 45 degrees to the base AB. This forms an isosceles triangle ABO with base angles of 45 degrees, making the height of O from AB equal to half the length of AB, which is 6/2 = 3.

AI explanation

Let the rectangle have vertices A(0,0), B(6,0), C(6,4) and D(0,4). The angle bisector of the 90 degree angle at A is the line y = x. The angle bisector at B is the line y = -x + 6. These lines meet at point O at (3,3). The distance of O from the length AB on the x-axis is the y-coordinate of O, which is 3.

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