Podcast
Questions and Answers
In a rhombus, what can be said about the diagonals?
In a rhombus, what can be said about the diagonals?
- They are perpendicular to each other (correct)
- They divide the rhombus into four congruent triangles
- They are parallel to each other
- They bisect each other
What is the property of concyclic points?
What is the property of concyclic points?
- They connect to form straight lines within the circle
- They are points of tangency with the circle
- They move along a line when a circle is rolled
- They are always on the circumference of the circle (correct)
What is the relationship between the sides of a parallelogram?
What is the relationship between the sides of a parallelogram?
- They are perpendicular
- They form angles of 90 degrees
- They are parallel and congruent (correct)
- They bisect each other
In a cyclic quadrilateral, what can be said about the opposite angles?
In a cyclic quadrilateral, what can be said about the opposite angles?
What is the property of the diagonals in a rectangle?
What is the property of the diagonals in a rectangle?
In a circle, what is the relationship between the angle formed by a chord and a tangent with the central angle it intercepts?
In a circle, what is the relationship between the angle formed by a chord and a tangent with the central angle it intercepts?
What is the measure of an angle inscribed in a semicircle?
What is the measure of an angle inscribed in a semicircle?
Which type of quadrilateral is said to be cyclic?
Which type of quadrilateral is said to be cyclic?
In a cyclic quadrilateral, what can be said about the opposite angles?
In a cyclic quadrilateral, what can be said about the opposite angles?
What special property do the diagonals of a square have?
What special property do the diagonals of a square have?
Flashcards
Tangent to a circle
Tangent to a circle
A line that touches a circle at only one point.
Angle between chord and tangent
Angle between chord and tangent
The angle formed between a chord and a tangent at the point of contact.
Angle of reflection
Angle of reflection
When two tangents are drawn from an external point to a circle, the angle between them.
Angle in a Semicircle
Angle in a Semicircle
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Cyclic Quadrilateral
Cyclic Quadrilateral
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Cyclic Square
Cyclic Square
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Cyclic Rectangle
Cyclic Rectangle
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Cyclic Rhombus
Cyclic Rhombus
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Cyclic Parallelogram
Cyclic Parallelogram
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Concyclic Points
Concyclic Points
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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.
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.
Rectangle
In a rectangle, two opposite sides are equal. Its diagonals bisect each other and are perpendicular.
Rhombus
All sides of a rhombus are equal, and opposite sides are parallel. Its diagonals are perpendicular to each other.
Parallelogram
Opposite sides of a parallelogram are parallel and congruent. Its diagonals divide the figure into four triangles, which are similar to each other.
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.
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