Class 10 Maths - HARYANA
Circles
The Class 10 Mathematics chapter on 'Circles' introduces students to fundamental geometric properties related to circles, tangents, and secants. For BSEH students, this chapter is crucial as it tests both theoretical understanding and logical reasoning through proofs. You will learn important theorems, such as the perpendicularity of the radius to the tangent at the point of contact, and the equality of lengths of tangents drawn from an external point. Mastering these concepts is essential for scoring high marks in geometry sections of the board exam.
Start Learning FreeKey Concepts
Secant and Tangent
A secant intersects a circle at two distinct points, whereas a tangent is a line that intersects the circle at exactly one point, known as the point of contact.
Radius and Tangent Theorem
The tangent at any point of a circle is perpendicular to the radius through the point of contact.
Tangents from an External Point
The lengths of tangents drawn from an external point to a circle are equal in length.
Number of Tangents
No tangent can be drawn to a circle from a point inside it, exactly one tangent can be drawn from a point on the circle, and exactly two tangents can be drawn from an external point.
Important Formulas
Board Exam Info
In the Haryana Board (BSEH) Class 10 Mathematics exam, the chapter 'Circles' typically carries around 4 to 6 marks. Common question types include 1-mark objective questions, 2-mark short answer proofs, and 4-mark long answer questions involving numerical calculations based on tangent properties and Pythagoras theorem.
Frequently Asked Questions
How many tangents can be drawn from a point inside a circle?
Zero tangents can be drawn from a point inside a circle because any line passing through an interior point will always intersect the circle at two points (becoming 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 it necessary to write the reasons for every step in geometry proofs in the BSEH exam?
Yes, writing reasons (like theorems or axioms used) in brackets next to your steps is mandatory to get full marks in geometry proofs.
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