The measure of angle ACB is less than the measure of the angle AOB.
GIven,
Making the conjecture.
What would happen to the angle formed if the vertex of angle AOB was moved from the center to point C, which lies on the circle is to be justify.
What is a circle?
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r². where h, k is the coordinate of the circle's center on coordinate plane and r is the circle's radius.
Here, there is a property of pair of lines,
when two lines intersect each other they hold some angle of intersection with each other, when the angle of intersection increases, assuming a point says the point of intercession getting close to the points then angle of the intersection will increase. If the point of intersection gets far away from that point, the angle of the intersection will decrease.
Similarly, in the given problem point O is close to the arc AB than C. Implies Angle ACB is smaller than Angle AOB.
Thus, the measure of angle ACB is less than the measure of the angle AOB.
Learn more about circle here:
brainly.com/question/11833983
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