Mathematics
Suppose you are given a circle. Describe a method by which you can find the center of this circle.
Answer
Steps of construction :
Draw two chords AB and CD in the given circle.
Draw XY, the perpendicular bisector of chord AB and MN, the perpendicular bisector of chord CD.
Mark point O, the intersection of perpendicular bisectors of both the chords.
Point O, is the center of the circle
Related Questions
Prove that equal chords of congruent circles subtend equal angles at their centers.
Draw two circles of different radii. How many points these circles can have in common? What is the maximum number of common points ?
Given two equal chords AB and CD of a circle, with center O, intersecting each other at point P. Prove that :
(i) AP = CP
(ii) BP = DP
In a circle of radius 10 cm, AB and CD are two parallel chords of lengths 16 cm and 12 cm respectively. Calculate the distance between the chords, if they are on :
(i) the same side of the center
(ii) the opposite side of the center