Maths-
General
Easy
Question
In △ABC, AD and are the bisectors of ∠A and ∠C respectively. AD and CE intersect at . If ∠ABC = 90^∘, then find ∠AOC.
Hint:
As we know AD and CE are angular bisectors we find ∠OAC and ∠OCA in terms of ∠A and ∠C .We find the value of ∠AOC by using the sum of angles in the triangle is 180°
The correct answer is: ∠AOC = 135°
![](data:image/png;base64,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)
Step 1:- find∠OAC and ∠OCA
In ABC ,
∠A+∠B+∠C = 180°(sum of angles in the triangle)
∠A+∠C = 180°- 90°
∠A+∠C = 90°
∠OAC = ½ ∠A (AD is angular bisector )
∠OCA = ½ ∠C (CE is angular bisector )
Step 2 :- Find ∠AOC
In AOC ,
∠AOC + ∠OAC + ∠OCA = 180°(sum of angles in the triangle)
∠AOC + ½ ∠A + ½ ∠C = 180°
∠AOC + ½ (∠A + ∠C) = 180° (Substitute ∠A+∠C = 90°)
∠AOC + ½ (90°) = 180° ∠AOC = 180°- 45° = 135°.
∴ ∠AOC = 135°
Step 1:- find∠OAC and ∠OCA
In ABC ,
Step 2 :- Find ∠AOC
In AOC ,
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, find
.
![](data:image/png;base64,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)
In the figure, sides QP and RQ of a
are produced to points S and T respectively.
If
and
, find
.
![](data:image/png;base64,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)
Maths-General
Maths-
Simplify √8 - √18 + √50
Simplify √8 - √18 + √50
Maths-General
Maths-
Maths-General
Maths-
Prove in the given figure, side QR of a
is produced to a point S.
If the bisector of
and
meet at the point T, then prove
![straight angle QTR equals 1 half straight angle QPR](data:image/png;base64,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)
![](data:image/png;base64,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)
Prove in the given figure, side QR of a
is produced to a point S.
If the bisector of
and
meet at the point T, then prove
![straight angle QTR equals 1 half straight angle QPR](data:image/png;base64,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)
![](data:image/png;base64,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)
Maths-General
Maths-
In an equilateral triangle ABC,D is a point on the side BC , such that
. Prove that
![9 AD squared equals 7 AB squared](data:image/png;base64,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)
In an equilateral triangle ABC,D is a point on the side BC , such that
. Prove that
![9 AD squared equals 7 AB squared](data:image/png;base64,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)
Maths-General
Maths-
In the figure, find the value of x.
![](data:image/png;base64,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)
In the figure, find the value of x.
![](data:image/png;base64,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)
Maths-General
Maths-
Maths-General
Maths-
Simplify √12 - √48 +√1323
Simplify √12 - √48 +√1323
Maths-General
Maths-
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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)
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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)
Maths-General