    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 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 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.  Suggest Corrections  0      Related Videos   Angle Bisector
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