Length of the chord the circle if length of the another chord which is equally inclined through the diameter is given
Given are two chords which are equally inclined through the diameter of the circle. Length of one chord is given. The task is to find the length of another chord.
Input: z = 48 Output: 48 degrees Input: z = 93 Output: 93 degrees
- Let AB and AC be the two chords of the circle having the center at O.
- now, in the figure we see,
OL is perpendicular to AB and OM is perpendicular to AC
- in triangle OLA and triangle OMA,
angle OLA = angle OMA = 90 degrees
angle OAL = angle OAM(as the chords are inclined equally through the diameter)
OA = OA(common side)
- so triangle OLA and triangle OMA are congruent to each other.
- So, OL = OM
- and we know, equal chords are equidistant from the center, so Length of AB and AC will be same.
If two chords are equally inclined through the diameter of the same circle, then they are of equal length.
Below is the implementation of the above approach:
The length is 48
Time Complexity: O(1)
Auxiliary Space: O(1)