Understand Tangent, Secant and Chord of a circle. Click on the link to Watch the VIDEO explanation:
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Tangent, Secant and Chord of a circle
Definition of Tangent, Secant and Chord of a circle
A line in the plane of a circle and having one and only one point common with it is known as tangent of the circle.
The common point is called the point of contact.
Here, O is the center of the circle, line l is the tangent and A is the point of Contact.
A line which intersects a circle at two points is called a secant to the circle.
Line m is the secant and it intersects the circle at A and B.
A segment whose endpoints lie on the circle is called a chord of the circle.
AB is the chord to the circle.
Understanding the theorem on arcs of circles. Click on the Link to Watch the VIDEO explanation:
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Theorem on Arcs of a circle.
In equal circles or in a same circles, if two arcs are subtend equal angles at the centers, they are equal.
Given AXB and CYD are equal circles with centres P and Q; arcs AMB and CND subtend equal angles angle APB and angle CQD.
To prove is that arc AMB is equal to arc CND
Proof is as follows:
Apply circle CYD to circle AXB so that centre Q falls on the centre P and QC along PA and D on the same side as B. Therefore, circle CYD overlaps circle AXB.
Therefore, C falls on A. Since circles are equal
Angle APB is equal to angle CQD. Given
Therefore, QD falls along PB.
Understand the meaning of Scalars and Vectors. click on the link to Watch the VIDEO explanation:
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Scalars and Vectors
A scalar quantity or briefly a scalar has a magnitude but is not related to any direction in space.
The fig. shows the liquids filled in a beaker and a bowl. The volume that this liquid occupies is a scalar as it has only magnitude and there is no direction.
Here in this fig. we see a thermometer is placed in a glass fill with liquid. With temperature of the liquid is shown in the thermometer is a scalar.
Mass is a scalar Quantity. Every real no is a scalar.
A vector is a physical Quantity which requires both magnitude and direction for its representation. Velocity is a vector.
Here we see motion of cars in different directions with common speed they are the examples of the vector.
Displacement is another example of a vector. Here we see the triangle ABC is shifted to a new position A dash, B dash, C dash. Movement of triangle ABC to new position A dash B dash C dash is an example of a vector.
Understand the construction of a square in a given circle. click on the link to Watch the Video explanation:
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To Construct a Square in a Given Circle
Steps:
First, Draw a circle with centre O.
Draw two diameters AC and BD so that the angle between them 360 degree divided by 4 is equal to 90 degrees which means that AC and BD are mutually perpendicular.
Draw the line segments AB, BC CD and DA.
ABCD is the required square in the given circle.
Understand Application of Integrals with the help of numerical. click on the link to Watch the VIDEO explanation: Watch Video
Application of Integrals - Problem 1
The Problem
Find the area enclosed between the parabolas y square is equal to 4ax and x square is equal to 4ay.
The Solution:
Points of intersection of the curves can be obtained by solving the equations.
y square is equal to 4ax and x square is equal to 4ay
Therefore, x is equal to 0 and x is equal to 4a.
Area enclosed between the given curves
A is equal to integral zero to 4a F1 of x minus F2 of x dx.
Therefore, the area is equal to 16a square by 3 square units.
Understand the meaning of Conic Sections. click on the link to Watch the VIDEO explanation: Watch Video
Conic Sections
When a solid is cut by a plane the curve common to the solid and the plane i.e. the curve which lies on the surface of the solid and the plane is called section of the solid by a plane.
Let's consider a rectangular parallelopiped
Drag the plane and cut the rectangular parallelopiped perpendicular to one of its faces. Click the button to see the sectional view.
The section i.e. seen is a rectangle.
Conics are the cross section of a cone when it is cut by a plane at different angles which are as shown
Drag the plane and cut the cone. Click on the button.
Now, you see the sectional view which shows an Ellipse whose axis is at the angle beta to the axis of the cone.
Drag the plane and cut the cone. Click on the button.
The sectional view which shows a parabola whose axis is inclined at an angle alpha to A A dash.
Drag the plane and cut the cone. Click on the button.
The sectional view which shows a hyperbola whose axis is inclined at an angle beta to the axis of the cone.
Understand Cyclic Quadrilateral. Click on the link to Watch the VIDEO explanation:
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Cyclic Quadrilateral
Draw a circle of with centre O. Mark four points A, B, C and D on the circumference of the circle.
Join A to B, B to C, C to D and D to A.
Thus, a quadrilateral ABCD is formed inside the circle.
Definition of the Cyclic Quadrilateral?
A quadrilateral is said to be cyclic if all its vertices lie on a circle. In the fig. A, B, C and D are the vertices of the cyclic quadrilateral.
Now let us know the important property of the Cyclic Quadrilateral.
In a cyclic quadrilateral, the opposite angles are supplementary. Therefore, in the fig. angle A plus angle C is equal to the 180 degrees and angle B plus angle D is equal to the 180 degrees.
