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
SSCClass 10 (SSC)Mathematics - Geometry (भूमिती)Ch 4 · Topic 1
Geometric Constructions
Advanced geometric constructions, like tangents to circles and similar triangles, require 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
Constructing a triangle similar to a given triangle with a specific scale factor involves proportionally extending or reducing its sides.
Why it matters
Division of a line segment in a given ratio uses the construction technique of drawing auxiliary lines and marking proportional points.
Key detail
Practising these constructions builds precision and deepens understanding of the geometric relationships being represented.
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Quick notes
• Tangent construction: uses radius perpendicularity.
• From an external point to the circle.
• Similar triangle construction: uses scale factor.
• Proportionally extend/reduce sides.
• Line segment division: given ratio.
• Uses auxiliary lines, proportional points.
• Practice builds construction precision.
• It deepens geometric relationship understanding.