Construction of an Angular Bisector and its Proof
Ashu has constructed the bisector of AB in such a way that AO=BO and AP=BP. The value of ∠AQO is
- Any where in the plane
- On the arms of the angle
- To the exterior of the angle
- To the interior of the angle
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.
- OX is angle bisector ∠AOB
- C is the midpoint of OX
- Two parallel lines
- Two perpendicular lines
- None of the above
- Two intersecting lines
Your aim is to construct an angle ∠ YPX = 30∘ using a compass and ruler only. What is the total number of arcs to be drawn to construct an angle of 30∘ after drawing the base ray PX?
- 3 arcs
- 4 arcs
- 6 arcs
- 5 arcs