Q1
What property helps construct a tangent from an external point?
ATangent perpendicular to radius at contact
BTangent parallel to radius
CNo specific property
DTangent equals radius length
ICSEClass 10 (ICSE)MathematicsCh 19 · Topic 1
Constructions (Circles)
Constructing circles and related elements, like tangents and inscribed/circumscribed circles, requires precise use of a compass and ruler.
Core concept
To construct a tangent to a circle from an external point, we use the property that the tangent is perpendicular to the radius at the point of contact.
How it works
An inscribed circle (incircle) of a triangle touches all three sides, with its centre found at the intersection of angle bisectors.
Why it matters
A circumscribed circle (circumcircle) passes through all three vertices of a triangle, with its centre found at the intersection of perpendicular bisectors of the sides.
Key detail
Practising circle constructions builds precision and understanding of the geometric relationships between circles, triangles, and their special points.
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Quick notes
• Tangent construction uses radius perpendicularity.
• Incircle touches all three triangle sides.
• Incircle centre: intersection of angle bisectors.
• Circumcircle passes through all three vertices.
• Circumcircle centre: intersection of perpendicular bisectors.
• These require precise compass and ruler use.
• Practice builds construction precision.
• This connects circles and triangles geometrically.