Angles, Chords, Radii, and Tangents
Aligned to G-C.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
Circle relationships connect angles to arcs. An inscribed angle equals half the central angle that subtends the same arc. A tangent line is perpendicular to the radius drawn to the point of tangency. An inscribed angle that subtends a diameter is a right angle.
Worked example
An inscribed angle subtends an arc of 80°. Find the inscribed angle. The inscribed-angle theorem says an inscribed angle is half the central angle (which equals its arc). So the inscribed angle = 80/2 = 40°. If a second inscribed angle subtends the same arc, it is also 40°, since all inscribed angles on the same arc are equal.
Practice questions
- A central angle measures 120°. Find the inscribed angle subtending the same arc.
- A triangle is inscribed in a circle with one side a diameter. What is the angle opposite that diameter?
- A tangent touches a circle at point T, and O is the center. What is the measure of angle OTP where P is on the tangent line?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Ángulos, cuerdas, radios y tangentes
Las relaciones del círculo conectan ángulos con arcos. Un ángulo inscrito es la mitad del ángulo central que subtiende el mismo arco. Una línea tangente es perpendicular al radio trazado al punto de tangencia. Un ángulo inscrito que subtiende un diámetro es un ángulo recto.
Ejemplo: Un ángulo inscrito subtiende un arco de 80°. Halla el ángulo inscrito. El teorema del ángulo inscrito dice que un ángulo inscrito es la mitad del ángulo central (que equivale a su arco). Así, el ángulo inscrito = 80/2 = 40°. Si un segundo ángulo inscrito subtiende el mismo arco, también mide 40°, pues todos los ángulos inscritos sobre el mismo arco son iguales.
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