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Class 9 Math Line Bisectors and Angle Bisectors


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3.ThreevillagesPQandRarenotonthesameline.ThepeopleofthesevillageswanttomakeaChildrenParkatsuchaplacewhichisequidistantfromthesethreevillages.AfterfixingtheplaceofChildrenParkprovethattheParkisequidistantfromthethreevillages.3. Three villages P Q and R are not on the same line. The people of these villages want to make a Children Park at such a place which is equidistant from these three villages. After fixing the place of Children Park prove that the Park is equidistant from the three villages.

2. Where will be the centre of a circle passing through three non-collinear points? And why?
2. Where will be the centre of a circle passing through three non-collinear points? And why?

2.Wherewillbethecentreofacirclepassingthroughthreenoncollinearpoints?Andwhy?2. Where will be the centre of a circle passing through three non-collinear points? And why?

5. In the given congruent triangles LMO and LNO
5. In the given congruent triangles LMO and LNO

5.InthegivencongruenttrianglesLMOandLNO5. In the given congruent triangles LMO and LNO

1. Prove that the bisectors of the angles of base of an isoscles triangle intersect each other on its altitude.
1. Prove that the bisectors of the angles of base of an isoscles triangle intersect each other on its altitude.

1.Provethatthebisectorsoftheanglesofbaseofanisosclestriangleintersecteachotheronitsaltitude.1. Prove that the bisectors of the angles of base of an isoscles triangle intersect each other on its altitude.

4. If the given triangle \mathrm{ABC} is equilateral triangle and \overline{\mathrm{AD}} is bisector of angle \mathrm{A} then find the values of unknowns x^{\circ} \dot{y}^{\circ} and z^{\circ} .
4. If the given triangle  \mathrm{ABC}  is equilateral triangle and  \overline{\mathrm{AD}}  is bisector of angle  \mathrm{A}  then find the values of unknowns  x^{\circ}   \dot{y}^{\circ}  and  z^{\circ} .

4.IfthegiventriangleABCisequilateraltriangleandADisbisectorofangleAthenfindthevaluesofunknownsxy˙andz.4. If the given triangle \mathrm{ABC} is equilateral triangle and \overline{\mathrm{AD}} is bisector of angle \mathrm{A} then find the values of unknowns x^{\circ} \dot{y}^{\circ} and z^{\circ} .

2. The bisectors of \angle \mathrm{A} \angle \mathrm{B} and \angle \mathrm{C} of a rilateral \mathrm{ABCP} meet each other at point \mathrm{O} . Prove that the bisector of \angle \mathrm{P} will also pass through the point \mathrm{O} .
2. The bisectors of  \angle \mathrm{A} \angle \mathrm{B}  and  \angle \mathrm{C}  of a rilateral  \mathrm{ABCP}  meet each other at point  \mathrm{O} . Prove that the bisector of  \angle \mathrm{P}  will also pass through the point  \mathrm{O} .

2.ThebisectorsofABandCofarilateralABCPmeeteachotheratpointO.ProvethatthebisectorofPwillalsopassthroughthepointO.2. The bisectors of \angle \mathrm{A} \angle \mathrm{B} and \angle \mathrm{C} of a rilateral \mathrm{ABCP} meet each other at point \mathrm{O} . Prove that the bisector of \angle \mathrm{P} will also pass through the point \mathrm{O} .

2. If \overleftarrow{\mathrm{CD}} is right bisector of line segment \overline{\mathrm{AB}} then(ii) \mathrm{m} \overline{\mathrm{AQ}}=
2. If  \overleftarrow{\mathrm{CD}}  is right bisector of line segment  \overline{\mathrm{AB}}  then(ii)  \mathrm{m} \overline{\mathrm{AQ}}=

2.IfCDisrightbisectoroflinesegmentABthen(ii)mAQ=2. If \overleftarrow{\mathrm{CD}} is right bisector of line segment \overline{\mathrm{AB}} then(ii) \mathrm{m} \overline{\mathrm{AQ}}=

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