Find the tangent at the given point.
- Compare center distance with r1+r2 and |r1−r2|; equal centers require separate treatment.
Skills and prerequisite lessons
Working and explanation
BUILD THE REASONING
Hint 1
Translate the geometric condition into a coordinate equation.
Hint 2
The radius is normal to the tangent.
Worked solution
Translate the geometric condition into a coordinate equation.
Apply the stated relation and retain its conditions.
Apply the stated relation and retain its conditions.
The point is on the circle and fixes the tangent constant.
The requested relation or conclusion is shown below.
Checks and common pitfalls: The point is on the circle and fixes the tangent constant.
Reasoning checklist · self / teacher assessment
- State a valid definition or model and its assumptions.
- Show the intermediate mathematical relations, not only the final claim.
- Check exclusions, units or the interpretation of the result.
Think first. Reveal a hint when the class is ready.