Find the Points of Intersection of Two Circles

Find the intersection points of two circles \((x - h_1)^2 + (y - k_1)^2 = r_1^2\) and \((x - h_2)^2 + (y - k_2)^2 = r_2^2\). Generate random problems, see detailed algebraic steps with exact values, and visualize both circles and their intersection points.

📐 Circle-Circle Intersection Finder

Find intersection points of two circles in center-radius form

Circle 1: \( (x)^2 + (y)^2 = 4 \), Circle 2: \( (x-3)^2 + y^2 = 4 \)
Find the intersection points (if any). Click "Show me" for each step.

📖 Step-by-Step Solution

STEP 1: Write equations of both circles
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STEP 2: Subtract equations to get the radical line
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STEP 3: Solve the radical line for y (or x)
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STEP 4: Substitute back into one circle equation
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STEP 5: Solve the quadratic and find intersection points
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📊 Graphical Visualization
Circle 1: Green | Circle 2: Blue | Intersection points: Red

Adjust axis scale to see the intersection points clearly.