Radius, diameter chord, tangent and secant associated with a circle
Q-1 Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?
Solution:
No common point.
Outer and Inner Circles Which Have No Common Point
Outer and inner circles with centers O and O' and no common point.
No point common
Two Circle That Center Point O and O'
The two circle that center point O and O' and its common point is P and Q
One point P is common
Circles Which Have a Single Common Point
Circle with centers O and O' and 1 common point.
One point P is common
Outer and Inner Circles Which Have a Single Common Point
Outer and inner circles with centers O and O' and 1 common point.
Two point P and Q are common
Circles Which Have a 2 Common Points
Circle with centers O and O' and 2 common point P and Q.
Infinite number of common points between two congruent and overlapping circles
Two Congruent and Overlapping Circles With Infinite Common Points
Two congruent and overlapping circles O and O' and infinite common point P and Q.
Therefore there can be infinite such points
Q-2 Suppose you are given a circle. Give a construction to find its centre.
Solution:
Circle With Center at a
Circle at center A and EF and GH are two chords.
Key idea: The key idea for solving this problems is to realize that the perpendicular bisector of chords of the circle pass through the center. So if we draw two perpendicular bisectors of two distinct chords they will intersect at the center of the circle. (The line joining the center and perpendicular to the chord, bisects the chord)
Following steps can be used to complete the construction:
Step 1 : Drawn the circle
Step 2 : EF and GH are two chords
Step 3: Draw the perpendicular bisectors of the chords EF and GH.
The point of intersection of two perpendicular bisector is the center of the circle.
