Let C be the mid-point of an arc AB-of a circle such that measure of arc
AB=183°. If the region
bounded by the arc ACB and line segment AB is denoted by S, then the centre of the
circle lies
(a) in the interior of S✔️
(b) in the exterior of S❌
(c)on the segment AB❌
(d) on AB and bisects AB❌
please don't tell direct answer i Know....i need explanation
Answers
This is very interesting question to solve! We should visualize the figure and draw it with the given details as prescribed in the quéstion.
Given:
❍ AB is an arc of circle
❍ C is the midpoint of arc AB
❍ Measure of arc AB = 183°
❍ Region bounded by the arc ACB and line segment AB is denoted by S.
To Find:
Where the centre of the circle lies?
Explanation:
Visual the picture, then start drawing the image.
First draw AB as an arc of a circle, then draw C as the midpoint of this arc AB. Now join A and B together at 183° and take that point O. Now we know that 180° = semi circle or in other words we can say that 180° means it is a semi circle, but here we have 180° angle that means shaded portion 'S' will be bigger than a semi circle.
So now, we have to find where point O i.e. , the centre of the circle lies?
In the figure, the shaded portion is 'S'. As it is given in the quéstion region bounded by the arc ACB and line segment AB is denoted by S so we will separate the portion 'S' from the entire circle.
Now, from the figure we can conclude that the center of the circle i.e., point 'O' lies in the interior of S portion.
∴ The centre of the circle lies in the interior of S
option ( a ) is correct ✅
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Answer:
Let C be the mid-point of an are AB of a circle such that mAB-183. If the region botinded by the urc ACB and line segment AB is denoted by S, then the centre O of the circin lies