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Featured 4 months ago

Coordinates of

Let the coordinates of B be

and coordinates of

as

as **(1)**, its slope is

and if **(2)**

and its intersection with **(1)** into **(B)**, we have

and

Hence, coordinates of point of intersection are

and hence

and coordinates of

graph{(3x+y+6)(x-3y-5)((x+1)^2+(y+3)^2-0.01)((x+1.6)^2+(y+1.2)^2-0.01)=0 [-9.92, 10.08, -5.88, 4.12]}

Featured 3 months ago

Let the equation of the circle which cuts the given parabola

Replacing

Here

Since the coefficient of **zero** , the sum of all 4 roots of y must be zero.

Hence

Featured 3 months ago

Area of a regular polygon

Perimeter

Since we know that the octagon is regular and we know the apothem (height from a side to the center of the polygon, we can calculate the side length):

Each angle of the central angle:

and each side of the polygon forms an isoceles triangle when joined to center. Further, a perpendicular from center to the side of the polygon divides the side in two equal parts and also cuts this angle at the center (

Using trigonometry, we can find half the side length (

side length:

Featured 2 months ago

length

We know that the perpendicular distance

Given that the two parallel lines are

Given that

Hence, length of each side of the equilateral triangle

Featured 3 weeks ago

As

Formula for the inradius (

where

or

Proof 1 :

Area

Proof 2 :

Recall that the tangents to a cicle from an external point are equal,

and

Featured 6 days ago

Please see below.

Let us consider the following figure, where we have the median

Now in

=

or **.....................(1)**

and in

=

or

But as

**.....................(2)**

Adding (1) and (2), we get

or

This is Apollonius theorem.

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