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 in D and C. Then he marks two more arcs with centres as C and D and radius more than 12 CD as shown (intersecting in Y) but has no idea why.
Select the statement which explains him 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 by SSS congruency criterion, △DOY is congruent to △COY.
So, corresponding parts of congruent triangles are equal which means, ∠ DOY = ∠COY and OY bisects the angle.
Hence, statement A is the one which gives the correct reason for OY being the angular bisector.