Maths-
General
Easy
Question
In △ABC, ∠B=90∘ and is the mid point of BC. Prove that ![A C squared minus A D squared equals 3 B D squared](data:image/png;base64,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)
The correct answer is: Hence proved
Hint :- use pythagoras theorem in triangle ABD and ABC
![](data:image/png;base64,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)
Hint :- use pythagoras theorem in triangle ABD and ABC
We get
and
subtract them and substitute BC = 2BD
In the equation to get the result.
Explanation(proof ) :-
Applying pythagoras theorem in triangle ABC,we get
—- Eq1
Applying pythagoras theorem in triangle ABD ,we get
Eq2
As AD is median , D is mid point then BC = 2BD
Subtract Eq1 - Eq2
We get, ![AC squared minus AD squared equals AB squared plus BC squared minus open parentheses AB squared plus BD squared close parentheses](data:image/png;base64,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)
![AC squared minus AD squared equals BC squared minus BD squared text substitute end text BC equals 2 BD](data:image/png;base64,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)
![AC squared minus AD squared equals 4 BD squared minus BD squared](data:image/png;base64,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)
![AC squared minus AD squared equals 3 BD squared](data:image/png;base64,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)
Hence proved
Related Questions to study
Maths-
Maths-General
Maths-
The perpendicular AD on the base BC of Triangle ABC intersects BC in D such that BD = 3CD. Prove that
![2 A B squared equals 2 A C squared plus B C squared](data:image/png;base64,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)
The perpendicular AD on the base BC of Triangle ABC intersects BC in D such that BD = 3CD. Prove that
![2 A B squared equals 2 A C squared plus B C squared](data:image/png;base64,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)
Maths-General
Maths-
In an equilateral
the side BC is trisected at D . Prove that ![9 A D squared equals 7 A B squared](data:image/png;base64,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)
.
In an equilateral
the side BC is trisected at D . Prove that ![9 A D squared equals 7 A B squared](data:image/png;base64,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)
.
Maths-General
Maths-
![](data:image/png;base64,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)
ABC and DBC are two isosceles triangles on the same base BC. Show
that ![straight angle ABD equals straight angle ACD](data:image/png;base64,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)
![](data:image/png;base64,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)
ABC and DBC are two isosceles triangles on the same base BC. Show
that ![straight angle ABD equals straight angle ACD](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHMAAAAOCAYAAAAc/yP5AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAANvpXuIwAAAjpJREFUeNrtmD9Iw1AQxkMIIuJSREqRIoiDFBGhiIOriDg4uIiDOHQRBwcXEXFyEwcnwUFEinQpnURcpIiTIE5FRBARh+LiICJFhPqdXKDU5v1J8xIpPfhRkqbNfd8l7917luU/pqx2tIQH+yAn+H5D8vsq8wLuQQH0eVxDfIN3cAQGW8QDin6wC+7AF3gA26AnLC8OwBsY9/h+lG86JClmbSyAa8k1JHCJBa9FXMggPJgFN2Aa2HwuATLgPAwvjiUiKLLgkFEtps1PpugaN+KgzCZEEUF4kAKPIKZ4z8C9yCqISPKwafHQkVRMjq67VRRAsQzyERQyKA/ozV7RuG+gXuQVRFg8/rtJ0ueOJDmbm4hLkNYQkOB5QzQfi/ATQXrw3KBH8FtMkRd/hr+CoohuHjo6+NgBT3xeZPgrGNYUYDUYlk2FCQ90c2/aC0dDhNu9bdWdo+N1QXIkehKcghENAWTwZwiFNOVBkMWUeuGwwaoiHI8JPcYdly1Jjrq+ooYAaslLhodZkx6I+gndYoq8+H1bzjREuJOwyLyMQnIVDQHUju8ZfCNNe0Dz6mpAxfT0opPXODoiLH4yBgQL45LC0uRDUUAvNxCmNg/C8CDJc2miyWJ6etEFLnyImFFojXN8XaPkSOgmr99EArp4c4Ha/nlDhQzTgzku6GJNwxTn46tmvSgqzjcu7lYWLSvGJELSdQnW/k+F128xyRZWmbewUgaH1zA9cHeK8ry0qPJDdAIm/oEX7YgyfgDzX/9iBs8sagAAAK10RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+JiN4MjIyMDs8L21pPjxtaT5BQkQ8L21pPjxtbz49PC9tbz48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+JiN4MjIyMDs8L21pPjxtaT5BQ0Q8L21pPjwvbWF0aD5Bmrz4AAAAAElFTkSuQmCC)
Maths-General
Maths-
PQ and RS are respectively the smallest and longest sides of a quadrilateral PQRS. Show that ∠ P > ∠ R
PQ and RS are respectively the smallest and longest sides of a quadrilateral PQRS. Show that ∠ P > ∠ R
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , justify. 3√24− 5√5
Classify whether the following Surd is rational or irrational , justify. 3√24− 5√5
Maths-General
Maths-
In △ABC, AD and are the bisectors of ∠A and ∠C respectively. AD and CE intersect at . If ∠ABC = 90^∘, then find ∠AOC.
In △ABC, AD and are the bisectors of ∠A and ∠C respectively. AD and CE intersect at . If ∠ABC = 90^∘, then find ∠AOC.
Maths-General
Maths-
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , justify 4√5+ 9
Classify whether the following Surd is rational or irrational , justify 4√5+ 9
Maths-General
Maths-
PQR is a triangle in which PQ=PR.S is any point on the side PQ. Through S, a line is drawn parallel to QR intersecting PR at T. Prove that PS = PT.
PQR is a triangle in which PQ=PR.S is any point on the side PQ. Through S, a line is drawn parallel to QR intersecting PR at T. Prove that PS = PT.
Maths-General
Maths-
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , justify 8-√48
Classify whether the following Surd is rational or irrational , justify 8-√48
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , Justify.√47+√8
Classify whether the following Surd is rational or irrational , Justify.√47+√8
Maths-General
Maths-
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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)
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