In a square ABCD, diagonals AC and BD intersect at O. The angle bisector of ∠ CAB meets BD and BC at F and G, respectively. OF : CG is equal to:

In a square ABCD, diagonals AC and BD intersect at O. The…

In a square ABCD, diagonals AC and BD intersect at O. The angle bisector of $\angle$ CAB meets BD and BC at F and G, respectively. OF : CG is equal to:

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. 1 : $\sqrt{2}$

Let the side of a square be x.

Diagonal of the square = $\sqrt2 x$ .

According to the angle bisector theorem in triangle ABC,

AB : AC = BG : GC = x : $\sqrt2 x$ = 1 : $\sqrt2$ ...............(1)

According to the angle bisector theorem in triangle ABO,

AB : OA = BF : FO = x : (x/ $\sqrt2$ ) = $\sqrt2$ : 1............(2)

In ratios 1 and 2, AB is not same so one needs to make AB same in both the ratio,

Multiply the first ratio by $\sqrt2$ we get

AB : AC = BG : GC = $\sqrt2$ : 2.

AB : OA = BF : FO = $\sqrt2$ : 1

OF : GC = 1 : $\sqrt2$ .

SSC CGL 2022 PYQ — Question 60