The change in point R as P is taken closer and closer to the x-axis.
The point R approaches the midpoint of radius when P is taken closer and closer to the x-axis.
Draw the vertical line from P to O in the given graph as shown below in Figure 1.
From Figure 1, the angle .
The triangle QOR is isosceles.
Let and .
The cosine law of the triangle QOR is,
From Figure 1, assume that the line .
The point P is closer and closer to the x-axis, that is, is approaching to 0, then approach zero and the value also approaches to zero.
If approaches to zero, then approaches to .
Since is a radius of the circle, .
If the point P is closer and closer to the x-axis, then x approach .
That is, R approach .
Therefore, the point R approaches the midpoint of radius .
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