ISEE Upper Level Math : Chords
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Example Questions
Example Question #21 : Circles
Figure NOT drawn to scale
In the above diagram, evaluate 
If two chords of a circle intersect inside the circle, the product of the lengths of the parts of each chord is the same. In other words,
Solving for 
Simplifying the radical using the Product of Radicals Principle, and noting that 25 is the greatest perfect square factor of 50:
Example Question #22 : Circles
In the above figure, 
Evaluate 
If a secant segment and a tangent segment are constructed to a circle from a point outside it, the square of the distance to the circle along the tangent is equal to the product of the distances to the two points on the circle along the secant; in other words,
and, substituting,
Distributing and writing in standard quadratic polynomial form,
We can factor the polynomial by looking for two integers with product 
By the Zero Product Principle,
Example Question #23 : Circles
Figure NOT drawn to scale
In the above diagram, evaluate 
If two chords of a circle intersect inside the circle, the product of the lengths of the parts of each chord is the same. In other words,
Solving for 
Simplifying the radical using the Product of Radicals Principle, and noting that the greatest perfect square factor of 96 is 16:
Example Question #24 : Circles
Figure NOT drawn to scale
In the above figure, 
Evaluate 
If a secant segment line and a tangent segment are constructed to a circle from a point outside it, the square of the length of the tangent is equal to the product of the distances to the two points on the circle intersected by the secant; in other words,
Substituting:
Distributing, then solving for 
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