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- Chapter 1- Rational and Irrational Numbers
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- Chapter 3- Compound Interest [Using Formula
- Chapter 4- Expansions
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- Chapter 6- Simultaneous Equations
- Chapter 7- Indices [exponents]
- Chapter 8- Logarithms
- Chapter 9- Triangles [Congruency in Triangles]
- Chapter 10- Isosceles Triangle
- Chapter 11- Inequalities
- Chapter 12- Mid-Point and Its Converse
- Chapter 13- Pythagoras Theorem
- Chapter 14- Rectilinear Figures
- Chapter 15- Construction of Polygons
- Chapter 16- Area Theorems
- Chapter 17- Circles
- Chapter 18- Statistics
- Chapter 19- Mean and Median
- Chapter 20- Area and Perimeter of Plane Figures
- Chapter 21- Solids
- Chapter 22- Trigonometrical Ratios
- Chapter 23- Trigonometrical Ratios of Standard Angles
- Chapter 24- Solution Of Right Triangles
- Chapter 25- Complementary angles
- Chapter 26- Co-ordinate Geometry
- Chapter 27- Graphical Solution
- Chapter 28- Distance Formula

The following figure shows a circle with center O.

Answer:

Solution

"hello students my name is rabbit singh
and i welcome you all to leader learning
homework one of india's best online
classes
now today in this video we have a
question that is based on the topic of
circle the question says the following
figure shows a circle with center o the
circle is given
and center o is given and sides are
given a
b points on the circle and o to
b we have drawn a perpendicular so if op
is perpendicular to a b then prove that
ap is equal to
p b that means this side will be equal
to this side
now first of all let us draw the
construction part
let us draw oa
and ob this is the external construction
that we are doing
now we will start the proof now you can
check
in triangles oap that means o
ap and triangle o b p
o a is equal to ob why because they are
radius
this and this are radii
this is also equal to radius so that's
why they are equal
now side op you can check this
perpendicular this is common
so that would be common now based on
right angle this is right angle so based
on right angle hypotenuse side
criteria of congruency triangle o
ap is congruent to triangle obp that we
have proved
now what we have to prove but ap is
equal to bp so
if you check these two triangles are
congruent so that means
ap will be equal to bp because y c b c d
corresponding parts of congruent
triangles so based on that
p becomes a midpoint of a b so hence
proof so i hope you have understood the
concept very clearly but still if you
have any doubt
do comment in the comment box and please
like and subscribe our channel for lido
thank you"

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