Question

Hari was asked to bisect a given angle, ∠ BOA as shown. He has done the following steps:

He draws an arc with centre O and some radius such that it cuts OB and OA at D and C respectively. Then he draws two more arcs with centres as C and D and radius more than 12CD as shown (intersecting at Y) but has no idea why.

Select the correct statement which explains to him the reason for his construction.

Statement A : Because of equal radius, DY = CY and OD = OC. So △ DOY is congruent to △ COY

Statement B : Since OC = OD, △ ODC in an isosceles triangle, base angles are equal.

- Statements A and B are true, only Statement A explains the reason.
- Statements A and B are true, only Statement B explains the reason.
- Statements A and B are true, but none explains the reason.
- Statements A and B are false.

Solution

The correct option is **A** Statements A and B are true, only Statement A explains the reason.

Since we take the same radius while marking the arcs from D and C, it is obvious that DY = CY.

Also, when we take O as the centre and any radius, we mark D and C so that OD = OC.

Now if we consider, OY is the side common to both of them.

So, △ DOY ≅ △ COY [by SSS congruency criterion]

⇒ ∠ DOY = ∠ COY [CPCT]

Hence, statement A is the one which gives the correct reason for OY being the angle bisector.

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