Given a circle with radius ‘r’ is given, the task is to find the diameter or longest chord of the circle.
Input: r = 4 Output: 8 Input: r = 9 Output: 18
Proof that the Longest chord of a circle is its Diameter:
- Draw circle O and any chord AB on it.
- From one endpoint of the chord, say A, draw a line segment through the centre. That is, draw a diameter.
- Now draw a radius from centre O to B.
- By the triangle inequality,
AB < AO + OB = r + r = 2r = d
- So, any chord that is not a diameter will be smaller than a diameter.
- So the largest chord is a diameter
- The Longest chord of any circle is its diameter.
- Therefore, the diameter of a circle is twice the radius of it.
Length of the longest chord or diameter = 2r
Below is the implementation of the above approach:
The length of the longest chord or diameter of the circle is 8
- Length of the chord the circle if length of the another chord which is equally inclined through the diameter is given
- Length of the chord of the circle whose radius and the angle subtended at the center by the chord is given
- Angle subtended by the chord to center of the circle when the angle subtended by the another equal chord of a congruent circle is given
- Find the other-end coordinates of diameter in a circle
- Find the center of the circle using endpoints of diameter
- Shortest distance from the centre of a circle to a chord
- Count ways to divide circle using N non-intersecting chord | Set-2
- Program to calculate angle on circumference subtended by the chord when the central angle subtended by the chord is given
- Find area of the larger circle when radius of the smaller circle and difference in the area is given
- Distance of chord from center when distance between center and another equal length chord is given
- Angle subtended by the chord when the angle subtended by another chord of same length is given
- Program to find Circumference of a Circle
- Program to find area of a circle
- Program to calculate area of inner circle which passes through center of outer circle and touches its circumference
- Find if a point lies inside a Circle
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