Why the angle between a tangent and a chord equals half its intercepted arc
In short: This video demonstrates the geometric proof that the angle formed by a tangent and a chord is exactly half the measure of the arc it intercepts. By constructing an isosceles triangle and applying circle properties, you can verify this relationship for both major and minor arcs.
The proof relies on the fundamental relationship between a circle's radius and its tangent line. By using these properties to build an isosceles triangle within the circle, the geometric logic confirms that the angle created at the intersection point is consistently half the intercepted arc's measure.
This geometric principle holds true regardless of whether the arc is a major or minor arc, providing a reliable rule for solving circle-based problems.
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Sources
- Summary by Intellect · source: Proof: Angle between a tangent and a chord | Geometry (TX TEKS) | Khan Academy
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