MathematicsChapter 6: Analytical Geometry
Tangent To A Circle
A tangent is perpendicular to the radius at contact; use the radius slope or tangent formula.
Learning objectives
- State the rule for tangent to a circle.
- Solve a tangent to a circle problem step by step.
- Check the result, restrictions, notation, and units.
Definition
A tangent is perpendicular to the radius at contact; use the radius slope or tangent formula.
Where / symbols
- Tangent to a circle
- A tangent is perpendicular to the radius at contact; use the radius slope or tangent formula.
CONCEPT AND RULE
A tangent is perpendicular to the radius at contact; use the radius slope or tangent formula.
METHOD
For tangent to a circle, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
For x2+y2=25 at (3,4), tangent is 3x+4y=25.
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve tangent to a circle
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Worked example
- Worked example:
- For x2+y2=25 at (3,4), tangent is 3x+4y=25.
In simple words
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Key points
- Tangent to a circle
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Tangent To A Circle
Sticky Notes · Formula and Worked Revision
Core Idea
- A tangent is perpendicular to the radius at contact; use the radius slope or tangent formula.
Rule / Formula
- A tangent is perpendicular to the radius at contact; use the radius slope or tangent formula.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- For x2+y2=25 at (3,4), tangent is 3x+4y=25.
Common Error
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
FBISE Exam Tip
- Show the formula, substitutions, algebra, restrictions, and final answer; method marks need visible reasoning.
60-second revision
- A tangent is perpendicular to the radius at contact; use the radius slope or tangent formula.
- Worked pattern: For x^2+y^2=25 at (3,4), tangent is 3x+4y=25.
- Final check: domain, sign, notation, units, and reasonableness.
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.