Circle diameter endpoints to radius (SAT). Game on.

Circle diameter endpoints to radius (SAT) is a grade 10 math skill aligned to Common Core standard HSG.GPE.A.1: derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 circle diameter endpoints to radius (sat) problems our math games drill.

CCSS HSG.GPE.A.110 questions in the bank
Kickoff

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Warm-upeasy

A circle in the coordinate plane has a diameter with endpoints (−6,−5)(-6, -5) and (−6,9).(-6, 9)\textsf{.} What is the radius of the circle?

The endpoints share the same xx-coordinate, so the diameter is vertical with length ∣9−(−5)∣=14.|9 - (-5)| = 14\textsf{.} The radius is half the diameter, so r=142=7.r = \dfrac{14}{2} = 7\textsf{.}

Mid-gameeasy

A circle in the coordinate plane has a diameter with endpoints (2,−4)(2, -4) and (18,−4).(18, -4)\textsf{.} What is the radius of the circle?

The endpoints share the same yy-coordinate, so the diameter is horizontal with length ∣18−2∣=16.|18 - 2| = 16\textsf{.} The radius is half the diameter, so r=162=8.r = \dfrac{16}{2} = 8\textsf{.}

Mid-gameeasy

A circle in the coordinate plane has a diameter with endpoints (8,0)(8, 0) and (8,6).(8, 6)\textsf{.} What is the radius of the circle?

The endpoints share the same xx-coordinate, so the diameter is vertical with length ∣6−0∣=6.|6 - 0| = 6\textsf{.} The radius is half the diameter, so r=62=3.r = \dfrac{6}{2} = 3\textsf{.}

Mid-gameeasy

A circle in the coordinate plane has a diameter with endpoints (−6,1)(-6, 1) and (12,1).(12, 1)\textsf{.} What is the radius of the circle?

The endpoints share the same yy-coordinate, so the diameter is horizontal with length ∣12−(−6)∣=18.|12 - (-6)| = 18\textsf{.} The radius is half the diameter, so r=182=9.r = \dfrac{18}{2} = 9\textsf{.}

Mid-gameeasy

A circle in the coordinate plane has a diameter with endpoints (2.5,−1)(2.5, -1) and (2.5,7).(2.5, 7)\textsf{.} What is the radius of the circle?

The endpoints share the same xx-coordinate, so the diameter is vertical with length ∣7−(−1)∣=8.|7 - (-1)| = 8\textsf{.} The radius is half the diameter, so r=82=4.r = \dfrac{8}{2} = 4\textsf{.}

Mid-gamemedium

A circle in the coordinate plane has a diameter with endpoints (0,0)(0, 0) and (6,8).(6, 8)\textsf{.} What is the radius of the circle?

The diameter length is (6−0)2+(8−0)2=36+64=100=10.\sqrt{(6 - 0)^2 + (8 - 0)^2} = \sqrt{36 + 64} = \sqrt{100} = 10\textsf{.} The radius is half the diameter, so r=102=5.r = \dfrac{10}{2} = 5\textsf{.}

Mid-gamemedium

A circle in the coordinate plane has a diameter with endpoints (1,−3)(1, -3) and (13,13).(13, 13)\textsf{.} What is the radius of the circle?

The diameter length is (13−1)2+(13−(−3))2=122+162=144+256=400=20.\sqrt{(13 - 1)^2 + (13 - (-3))^2} = \sqrt{12^2 + 16^2} = \sqrt{144 + 256} = \sqrt{400} = 20\textsf{.} The radius is half the diameter, so r=202=10.r = \dfrac{20}{2} = 10\textsf{.}

Buzzer beatermedium

A circle in the coordinate plane has a diameter with endpoints (−5,2)(-5, 2) and (5,26).(5, 26)\textsf{.} What is the radius of the circle?

The diameter length is (5−(−5))2+(26−2)2=102+242=100+576=676=26.\sqrt{(5 - (-5))^2 + (26 - 2)^2} = \sqrt{10^2 + 24^2} = \sqrt{100 + 576} = \sqrt{676} = 26\textsf{.} The radius is half the diameter, so r=262=13.r = \dfrac{26}{2} = 13\textsf{.}

Overtime

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Tests that cover circle diameter endpoints to radius (sat):
NAEPSATACTNY State MathNC EOG/EOC
Reporting domains for this skill
SAT All grades: Geometry and TrigonometryACT All grades: Preparing for Higher MathNAEP Grade 12: Measurement and GeometryACT Aspire All grades: Preparing for Higher MathATLAS Geometry: CirclesATLAS Geometry: Expressing Geometric Properties with Equations
More Grade 10 skills
Two-event conditional probability word problems (SAT)Advanced area formulasCircle equation translations (ACT/SAT/PSAT 8/9/10)Normal distribution basicsUnit circle trig values (SAT)Possible coordinates on a circle (SAT)Equation of a circleMidpoint formulaAll Grade 10 practice →

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