GEOMETRY. BY: Harvandeep Shergill Ricmond Simran. Introduction. Hi , I am Harvandeep Shergill people call me Venus. I am in Grade 11 and 17 years old. Math is my favorite subject.
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Problem: Find the center and radius of (x - 2)2 + (y + 3)2 = 16. Then graph the circle.
Solution: Rewrite the equation in standard form. (x - 2)2 + [y - (-3)]2 = 42 The center is (2, -3) and the radius is 4. The graph is easy to draw, especially if you use a compass. The figure below is the graph of the solution.
Radii of a circle
Radii of a circle is any line originationg from the centre of a circle to the point on the circumference of a circle.Eg In the image shown below a , b , c are the radii.
Central angle of a circle
Central angle is an angle formed by joining two points on the circumference of a circle to the center of the circle.Eg as shown below
A,B are two points on circumference of the circle and O is the centre of a circle. Threfore Angle AOB is Central angle of this Cirlce
Chord of a circle-
Chord of a circle is a geometrical line segment whose endpoints joins curve of a circle.
Find x in each of the following figures in Figure
Let there be a triangle ABC
Draw a line from A to mid point of BC(X) i.e. perpendicular to BC
In triangle AXB and AXC
Angle AXB = Angle AXC ( 90 degree each)
CX=XB (X is Mid point)
Therefore, Triangle AXB ~= Triangle AXC
Angle ACX = Angle ABX
Draw a line from C to midpoint of AB(Y) i.e. perpendicular to AB
In triangle BCY and ACY
Angle CYB = Angle CYA ( 90 degree each)
BY=AY (Mid point)
Therefore, Triangle BCY ~= Triangle ACY
Angle CBY = Angle CAY
Draw a line from B to midpoint of AC(Z) i.e. perpendicular to AC
So AB=BC=AC (all side to polygon ABC are equal)
Also Angle ACB=Angle ABC, Angle CAB=Angle CBA, Angle BAC=Angle BCA
So Angles ACB=ABC=BAC (Proved all angles of Polygon are equal)
Two triangles are formed AZB & CZB
In triangle AZB and CZB
Angle AZB = Angle CZB ( 90 degree each)
CZ=ZA (Mid point)
Therefore, Triangle AZB ~= Triangle CZB
Angle ZCB = Angle ZAB