Maths-
General
Easy
Question
In
, the bisectors of
and
intersect each other at O. Prove that
![90 to the power of ring operator plus 1 half straight angle A](data:image/png;base64,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)
Hint:
As we know OB and OC are angular bisectors we find ∠OBC and ∠OCB in terms of ∠A and ∠B .We find the value of ∠BOC by using the sum of angles in the triangle is 180°.
The correct answer is: Hence proved
Aim :- Prove ![straight angle B O C equals 90 plus 1 half straight angle A](data:image/png;base64,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)
![](data:image/png;base64,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)
Step 1:- Find ∠OBC and ∠OCB
∠OBC =
∠B(OB is the angular bisector)
∠OCB =
∠C (OC is the angular bisector)
∠A+ ∠B+ ∠C =180° (sum of angles in triangle ABC)
∠B+ ∠C =180°-∠A
Step 2:- Find ∠BOC
∠BOC+ ∠OBC + ∠OCB =180° (sum of angles in triangle OBC)
∠B+ ∠C =180°-∠A
Step 2:- Find ∠BOC
∠BOC+ ∠OBC + ∠OCB =180° (sum of angles in triangle OBC)
∠BOC+
∠B +
∠C = 180°
∠BOC= 180° -(
∠B +∠C )
∠BOC= 180°-(
∠B +∠C)
∠BOC= 180°-(
180°-∠A)
![not stretchy rightwards double arrow straight angle B O C equals 90 to the power of ring operator plus 1 half straight angle A](data:image/png;base64,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)
Hence proved
Step 1:- Find ∠OBC and ∠OCB
∠OBC =
∠OCB =
∠A+ ∠B+ ∠C =180° (sum of angles in triangle ABC)
∠B+ ∠C =180°-∠A
Step 2:- Find ∠BOC
∠BOC+ ∠OBC + ∠OCB =180° (sum of angles in triangle OBC)
∠B+ ∠C =180°-∠A
Step 2:- Find ∠BOC
∠BOC+ ∠OBC + ∠OCB =180° (sum of angles in triangle OBC)
∠BOC+
∠BOC= 180° -(
∠BOC= 180°-(
∠BOC= 180°-(
Hence proved
Related Questions to study
Maths-
and are the medians of a
right angled at . Prove that
.
and are the medians of a
right angled at . Prove that
.
Maths-General
Maths-
In
right angled at A, AL is drawn perpendicular to BC. Prove that
.
![](data:image/png;base64,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)
In
right angled at A, AL is drawn perpendicular to BC. Prove that
.
![](data:image/png;base64,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)
Maths-General
Maths-
Simplify √50 - √98 + √162
Simplify √50 - √98 + √162
Maths-General
Maths-
A fish tank is in the shape of a cube . Its volume is 125 Cubic feet . What is the area of one face of the tank ?
A fish tank is in the shape of a cube . Its volume is 125 Cubic feet . What is the area of one face of the tank ?
Maths-General
Maths-
In the adjacent figure, points B, A, D are collinear and AD = AC.
Given that
and
. Find
.
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)
In the adjacent figure, points B, A, D are collinear and AD = AC.
Given that
and
. Find
.
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)
Maths-General
Maths-
In the figure, ABC is a triangle in which
. Show that ![A C squared equals A B squared plus B C squared minus 2 B C times B D](data:image/png;base64,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)
.![](data:image/png;base64,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)
In the figure, ABC is a triangle in which
. Show that ![A C squared equals A B squared plus B C squared minus 2 B C times B D](data:image/png;base64,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)
.![](data:image/png;base64,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)
Maths-General
Maths-
Solve the equation m2 = 14
Solve the equation m2 = 14
Maths-General
Maths-
The traversers are adding a new room to their house. The room will be a cube with a volume of 6589 cubic feet .They are going to put in hardwood floors , which costs Rs 10 per square foot . How much will the hardwood floors cost ?
The traversers are adding a new room to their house. The room will be a cube with a volume of 6589 cubic feet .They are going to put in hardwood floors , which costs Rs 10 per square foot . How much will the hardwood floors cost ?
Maths-General
Maths-
Maths-General
Maths-
The angles of a triangle are
Find the value of and then the angles of the triangle
The angles of a triangle are
Find the value of and then the angles of the triangle
Maths-General
Maths-
D and E are points on the base BC of
such that BD = CE. If AD = AE, prove that
.
![](data:image/png;base64,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)
D and E are points on the base BC of
such that BD = CE. If AD = AE, prove that
.
![](data:image/png;base64,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)
Maths-General
Maths-
Sita has a square shaped garage with 228 square feet of floor space. She plans to build an addition that will increase the floor space by 50%. What will be the length of one side of new garage ?
Sita has a square shaped garage with 228 square feet of floor space. She plans to build an addition that will increase the floor space by 50%. What will be the length of one side of new garage ?
Maths-General
Maths-
Maths-General
Maths-
In
, DA = DB = DC. Show that
.
![](data:image/png;base64,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)
In
, DA = DB = DC. Show that
.
![](data:image/png;base64,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)
Maths-General
Maths-
In the figure, if
and
find x and y.
![](data:image/png;base64,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)
In the figure, if
and
find x and y.
![](data:image/png;base64,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)
Maths-General