Florida B.E.S.T. MA.912.GR.6.1

MathGrades 9–12Use properties and theorems related to circles.

The Standard

Solve mathematical and real-world problems involving the length of a secant, tangent, segment or chord in a given circle.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students identify which chord, secant, or tangent relationship fits a diagram or situation. They set up a product equation, solve for the missing length, and interpret the result in context.
What Mastery Looks Like: Students label inside, outside, and whole lengths correctly from a diagram. They choose the matching circle relationship, solve the equation, and check that the answer is reasonable and positive.
Common Misconceptions: Students often use only the inside part of a secant instead of the whole secant length. They may forget to square the tangent length or multiply the wrong chord pieces. Some choose a negative root even though a length must be positive.
How to Assess It: Exit ticket: From point P, a tangent has length x, while a secant has an outside length of 4 and an inside length of 5. Write an equation and find x.

Lesson moves

Draw two intersecting chords on paper circles, measure all four pieces with rulers, and compare the products of paired lengths.
Ask students to explain in writing why a secant calculation uses the outside length times the whole length.
Run a card sort matching circle diagrams, equations, and missing-length solutions for chords, secants, and tangents.
Use a map of a circular pond to calculate the length of a tangent walking path from a point outside the pond.

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