Class 10 Maths - ICSE
Constructions (Circles)
The Constructions chapter focusing on Circles in Class 10 ICSE Mathematics teaches students how to draw precise geometric figures using a ruler and compass. Specifically, you will learn how to construct tangents to a circle from an external point, circumscribe and inscribe circles in triangles and polygons, and locate centres of circles. This chapter is highly visual and carries significant weight in the ICSE board exams. Mastering these step-by-step construction techniques ensures full marks in the drawing sections, requiring accuracy with compasses, sharp pencils, and clean construction arcs without erasure marks.
Start Learning FreeKey Concepts
Tangent from an External Point
Drawing line segments from a point outside the circle such that they touch the circle at exactly one point, requiring the perpendicularity of the radius to the tangent.
Circumcircle of a Triangle
Constructing a circle that passes through all three vertices of a triangle by finding the circumcentre through the intersection of perpendicular bisectors of the sides.
Incircle of a Triangle
Constructing a circle inside a triangle that touches all three sides by locating the incentre using the angle bisectors of the interior angles.
Circumscribing and Inscribing Regular Polygons
Constructing circles related to regular polygons, such as hexagons, by dividing the 360-degree center angle into equal parts based on the number of sides.
Locating the Centre of a Circle
Finding the unknown center of a given circular arc or complete circle by drawing two non-parallel chord perpendicular bisectors.
Important Formulas
Board Exam Info
In the ICSE Class 10 Mathematics examination, constructions typically appear as a compulsory or choice-based 4-mark question in Section B. Questions almost always involve drawing tangents to a circle, circumcircles, or incircles. Examiners strictly check construction lines, arcs, and the neatness of the final diagram.
Frequently Asked Questions
Are construction lines required to be left visible in the final exam?
Yes, all construction arcs and lines must be clearly visible and should not be erased, as examiners use them to verify your method.
What drawing instruments are mandatory for this chapter?
A sharp pencil (preferably 2H or H), a scale/ruler, a compass, and a divider are essential for high accuracy.
How do I find the number of tangents from a point inside a circle?
No tangents can be drawn from a point inside a circle because any line passing through it will be a secant intersecting the circle at two points.
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