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.