Using radius-tangent angle relationship
At the point where a tangent touches a circle, the radius to that point makes a right angle with the tangent.
Practice This ConceptMain explanation
Teacher explanation
This property helps in angle chasing. If one angle in a circle figure depends on the tangent, you can immediately replace it with 90 degrees. Then the rest of the angles often follow by simple angle rules.
Example
If OA is a radius and AT is tangent at A, then angle OAT is 90 degrees.
Simple analogy
Touch point plus radius equals right angle.
Common confusion
Students often treat the angle as unknown and try to calculate it from scratch, even when the tangent rule already gives it.
Exam tip
When a radius meets a tangent at the point of contact, write 90 degrees first and save time.
Answer writing and exam use
1-mark use
Write the exact meaning of using radius-tangent angle relationship in one clean line.
2-mark use
Define using radius-tangent angle relationship and add one example or condition.
3-mark use
Explain using radius-tangent angle relationship, show the method or example, and mention the common mistake.
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