Practice Tangent Intuition in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A line that just barely touches a curve at exactly one point without crossing it, matching the curve's direction at that point.
A basketball resting on a flat floor—the floor touches the ball at exactly one point.
Example 1
mediumFind the equation of the tangent line to the circle x^2 + y^2 = 25 at point P(3, 4).
Example 2
hardFrom external point Q(7, 0), find the length of the tangent to the circle x^2 + y^2 = 25.
Example 3
mediumVerify that the line y = x + 5\sqrt{2} is tangent to the circle x^2 + y^2 = 25, and find the point of tangency.
Example 4
easyAt what angle does the tangent to a circle meet the radius drawn to the point of tangency? Use this to explain why a tangent touches the circle at only one point.