Circles in ICSE Class 10 Maths

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In a rhombus, what can be said about the diagonals?

They are perpendicular to each other

What is the property of concyclic points?

They are always on the circumference of the circle

What is the relationship between the sides of a parallelogram?

They are parallel and congruent

In a cyclic quadrilateral, what can be said about the opposite angles?

Their sum is 360 degrees

What is the property of the diagonals in a rectangle?

They are perpendicular to each other

In a circle, what is the relationship between the angle formed by a chord and a tangent with the central angle it intercepts?

They are equal

What is the measure of an angle inscribed in a semicircle?

90 degrees

Which type of quadrilateral is said to be cyclic?

Square

In a cyclic quadrilateral, what can be said about the opposite angles?

They add up to 180 degrees

What special property do the diagonals of a square have?

They intersect at a right angle

Study Notes

Circles in ICSE Class 10 Maths

Circles are essential geometrical shapes that play a significant role in various mathematical concepts. In the ICSE Class 10 Maths curriculum, circles are studied extensively, with emphasis on tangent properties, angles in a circle, cyclic quadrilaterals, and concyclic points. Here is an overview of these topics.

Tangents to a Circle

A tangent line intersects a circle exactly once, touching its circumference without crossing it. The angle between the chord and the tangent is equal to the central angle it intercepts. When two tangents are drawn from an external point to a given circle, the angle between them is called the angle of reflection.

Tangent to a Circle

Angles in a Circle

An angle inscribed in a semicircle measures 90 degrees. Similarly, an angle subtended by a diameter is also 90 degrees. If two angles are inscribed in one semicircle, they are supplementary to each other.

Cyclic Quadrilaterals

A quadrilateral is said to be cyclic if all its vertices lie on a single circle. There are four types of cyclic quadrilaterals based on the side lengths: square, rectangle, rhombus, and parallelogram.

Square

A square is a special case of a cyclic quadrilateral where all sides are equal. It can be shown that the diagonals bisect each other in a square.

Square Diagonal Bisectors

Rectangle

In a rectangle, two opposite sides are equal. Its diagonals bisect each other and are perpendicular.

Rectangle Diagonal Bisectors

Rhombus

All sides of a rhombus are equal, and opposite sides are parallel. Its diagonals are perpendicular to each other.

Rhombus Diagonals

Parallelogram

Opposite sides of a parallelogram are parallel and congruent. Its diagonals divide the figure into four triangles, which are similar to each other.

Parallelogram Diagonals

Concyclic Points

Concyclic points are those points that move along a circle when the circle is rolled along a straight line. Two tangents drawn from different points outside a circle meet at a point, and this point is called the center of contact.

For more information on these topics and their applications in mathematics, refer to your textbook or consult your teacher.

Explore the fundamental topics related to circles in ICSE Class 10 Maths, including tangent properties, angles in a circle, cyclic quadrilaterals like squares, rectangles, rhombuses, and parallelograms, and the concept of concyclic points. Enhance your understanding of these geometrical concepts with detailed explanations and diagrams.

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