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In the given diagram, PT is tangent to circle O and PN intersects circle O at J. Find the radius of the circle.
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| Photo by Math Principles in Everyday Life |
Solution:
Consider the given figure above
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| Photo by Math Principles in Everyday Life |
As you can see from the figure, it is hard to solve for the radius of a circle. We have to do something in the given figure first. Let's extend the given line segment PN so that it will meet the other side of a circle at point R and then label further the given figure as follows
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| Photo by Math Principles in Everyday Life |
If a theorem says "When a secant segment and a tangent segment are drawn to a circle from an external point, the product of the secant segment and its external segment is equal to the square of the tangent segment.", then the working equation for circle O is
Hence, the value of y which is one-half of the chord or line segment JR is
and the value of x is
By Pythagorean Theorem, the value of d which is the perpendicular distance of a chord to the center of a circle is
Therefore, by Pythagorean Theorem also, the radius of a circle is
