Q1
What is a tangent's relationship to the radius?
APerpendicular at the point of contact
BParallel always
CEqual in length
DNo relationship
ICSEClass 10 (ICSE)MathematicsCh 18 · Topic 1
Tangents and Intersecting Chords
A tangent touches a circle at one point, and intersecting chords and tangent-secant relationships follow specific theorems useful for solvin
Core concept
A tangent to a circle is perpendicular to the radius at the point of contact, a fundamental tangent property.
How it works
When two chords intersect inside a circle, the products of their segments are equal: if chords AB and CD intersect at P, then AP×PB = CP×PD.
Why it matters
The tangent-secant relationship states that the square of the tangent length equals the product of the secant's external and total lengths.
Key detail
Understanding these theorems helps solve various circle geometry problems involving tangent lines, chords, and their relationships.
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Quick notes
• A tangent is perpendicular to the radius at contact.
• Intersecting chords: AP×PB = CP×PD.
• Tangent-secant: tangent² = external × total secant length.
• These are key circle theorems.
• They involve tangents, chords, secants.
• They help solve circle geometry problems.
• Practice builds theorem application skills.
• These theorems connect various circle properties.