Given a circle in which the width and height of an arc are given. The task is to find the radius of the circle with the help of the width and height of the arc.
Input: d = 4, h = 1 Output: The radius of the circle is 2.5 Input: d = 14, h = 8 Output: The radius of the circle is 7.0625
- Let the radius of the circle be r
- Let the height and width of the arc be h & d
- Now, the diameter DC bisects the chord AB in two halves, each having length d/2
- Also the diameter is divided by the chord in two parts, the part inside arc h and the remaining 2r-h
- Now from intersecting chords theorem,
h*(2r-h) = (d/2)^2
or, 2rh – h^2 = d^2/4
so, r = d^2/8h + h/2
- So, radius of the circle
The radius of the circle is 2.5
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.
In case you wish to attend live classes with industry experts, please refer DSA Live Classes