Given a circle whose chord and tangent meet at a particular point. The angle in the alternate segment is given. The task here is to find the angle between the chord and the tangent.
Input: z = 48 Output: 48 degrees Input: z = 64 Output: 64 degrees
- Let, angle BAC is the given angle in the alternate segment.
- let, the angle between the chord and circle = angle CBY = z
- as line drawn from center on the tangent is perpendicular,
- so, angle OBC = 90-z
- as, OB = OC = radius of the circle
- so, angle OCB = 90-z
- now, in triangle OBC,
angle OBC + angle OCB + angle BOC = 180
angle BOC = 180 – (90-z) – (90-z)
angle BOC = 2z
- as angle at the circumference of a circle is half the angle at the centre subtended by the same arc,
so, angle BAC = z
- hence, angle BAC = angle CBY
Below is the implementation of the above approach:
The angle between tangent and the chord is 48 degrees
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