Proof of Tangent Circle Construction

Given: Circles P, A, and O, Isoceles Triangle QOB

Oval Q tangent to Circles O at C and P at A

Circle A equal to Circle O


Proof: Oval Q is in fact a circle.

Need to show that QC = QA


QO = QB by definition of Isoceles Triangle

QO = QC + CO and QB = QA + AB by segment addition

by substitution we know QC + CO = QA + AB

CO = AB since circle O = circle A therefore their respective radius must be equal.

by substitution QC + AB = QA + AB

by subtraction QC = QA.