- Introduction of Loci
Construct a triangle ABC, having given AB = 4.8 cm, AC = 4cm, and ∠A = 75°.
Find a point P.
(i) Inside the triangle ABC.
(ii) outside the triangle ABC
Equidistant from B and C; and at a distance of 1.2 cm from BC.
The locus of points within a circle that are equidistant from the end points of a given chord.
The locus of the centres of all circles that are tangent to both the arms of a given angle.
The locus of the centres of a given circle which rolls around the outside of a second circle and is always touching it.
Construct a triangle ABC in which angle ABC = 75°, AB= 5cm and BC =6.4cm. Draw perpendicular bisector of side BC and also the bisector of angle ACB. If these bisectors intersect each other at point P; prove that P is equidistant from B and C; and also from AC and BC.
Given: AX bisects angle BAC and PQ is perpendicular bisector of AC which meets AX at point Y.
Prove: (i) X is equidistant from AB and AC.
(ii) Y is equidistant from A and C.