SME
Grade 10 Math
Circles: arcs, chords, tangents and inscribed angles
The main lesson, then each kind of problem it solves.
Circles: arcs, chords, tangents and inscribed angles
Main lesson
The angle in a semicircle
Use this for “AB is a diameter and m∠PAB = 34°. Find m∠PBA.”
A tangent and its radius
Use this for “The radius is 8 and the tangent from P is 15. How far is P from the center?”
Two chords crossing
Use this for “Chords AB and CD cross at E; AE = 6, EB = 4 and CE = 3. Find ED.”
Two secants from a point
Use this for “From P, PA = 3 and PB = 10 on one secant, PC = 5 on the other. Find PD.”
A tangent and a secant from a point
Use this for “From P, PA = 4 and PB = 16 on a secant. How long is the tangent PT?”
Opposite angles of an inscribed quadrilateral
Use this for “ABCD is inscribed in a circle and m∠A = 84°. Find m∠C.”
Angles from arcs
Use this for “Two chords cross inside a circle, cutting off arcs of 70° and 110°. Find the angle.”