Class 10 Maths - ODISHA
Circles
The 'Circles' chapter in Class 10 Mathematics for the Odisha BSE board builds upon basic geometric properties learned in earlier classes. It introduces students to fundamental concepts regarding the interaction between a circle and lines, specifically secants and tangents. You will learn important theorems concerning the length of tangents drawn from an external point and how the tangent at any point of a circle is perpendicular to the radius through the point of contact. This chapter is highly scoring and carries significant weight in the board examinations, often featuring both direct theorem proofs and numerical application problems.
Start Learning FreeKey Concepts
Secant and Tangent
A secant is a line that intersects a circle at two distinct points, whereas a tangent is a line that touches the circle at exactly one point, known as the point of contact.
Tangent Perpendicular to Radius
The tangent at any point of a circle is perpendicular to the radius through the point of contact, forming a 90-degree angle.
Tangents from an External Point
The lengths of tangents drawn from an external point to a circle are equal in length, creating congruent triangles.
Number of Tangents
No tangent can be drawn from a point inside a circle, exactly one tangent can be drawn from a point on the circle, and exactly two tangents can be drawn from a point outside the circle.
Important Formulas
Board Exam Info
In the Odisha BSE Class 10 Mathematics board exam, the Circles chapter typically carries around 6 to 8 marks. Questions usually include 1-mark objective questions, 2-mark short answer theorem proofs, and 3-to-4-mark long answer numerical problems based on tangent properties.
Frequently Asked Questions
How many tangents can be drawn from a point inside a circle?
Zero tangents can be drawn from a point located inside a circle because any line passing through an interior point will always act as a secant.
Are the two tangents drawn from an external point always equal?
Yes, the lengths of tangents drawn from an external point to a circle are always equal.
Is the proof of the tangent theorem important for BSE Odisha exams?
Yes, proving that the tangent at any point of a circle is perpendicular to the radius through the point of contact is a very frequently asked question in board exams.
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