Question

State the locus of a point in a rhombus ABCD, which is equidistant

(i) from AB and AD;

(ii) from the vertices A and C.

Answer 1

Steps of Construction:

i) In rhombus ABCD, draw angle bisector of which meets in C.

ii) Join BD, which intersects AC at O.

O is the required locus.

iii) From O, draw and

In

( AC is bisector of angle A)

AO = OA (Common)

Therefore, O is equidistant from AB and AD.

Diagonal AC and BD bisect each other at right angles at O.

Therefore, AO = OC

Hence, O is equidistant from A and C.