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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 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 correct statement which explains him the reason.

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

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


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

Statements A and B are true, only Statement B explains the reason.

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C

Statements A and B are true, but none explains the reason.

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D

Statements A and B are false.

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Solution

The correct option is A Statement A : Because of equal radius, DY = CY and OD = OC. So ∆DOY is congurent to ∆COY

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 bisect the angle.

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


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