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Chapter 5: Circles and Loci

When you combine secants, chord, and tangents, angles are formed. Followings are some properties of these angles:

The measure of an angle formed by two secants or chords intersecting in the interior of a circle is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

The measure of an angle formed by two secants intersecting the exterior of the circle is one-half the difference of the measures of the intercepted arcs.

If a tangent and a secant or a chord intersects at the point of tangency on a circle, then the measure of the angle formed is one-half the measure of its intercepted arc.

The measure of an angle formed either by a tangent and a secant intersecting at a point exterior to a circle,

or

1.   two tangents intersecting at a point exterior to a circle equals one-half the difference of the measures of the intercepted arcs.
1.   If two chords of a circle intersect, then the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord.

If a tangent and a secant intersect in the exterior of a circle, then the square of the length of the tangent segment equals the product of the lengths of the secant segment and the external secant segment.

If two secants intersect in the exterior of a circle, then the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment.

# Circle on Coordinate Plane

When you want to represent a circle on a coordinate plane, you need to use the following equation: (x-h)^2 + (y-k)^2 = r^2, where h and k are the center points of the circle and r is the radius or the circle.

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