Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

In △ABC, ∠B=90^∘ and is the mid point of BC. Prove that $A C squared minus A D squared equals 3 B D squared$

The correct answer is: Hence proved

Hint :- use pythagoras theorem in triangle ABD and ABC

Hint :- use pythagoras theorem in triangle ABD and ABC
We get $AC squared$ and $AD squared$ subtract them and substitute BC = 2BD
In the equation to get the result.
Explanation(proof ) :-
Applying pythagoras theorem in triangle ABC,we get
$A C squared equals A B squared plus B C squared$ —- Eq1
Applying pythagoras theorem in triangle ABD ,we get
$AD squared equals AB squared plus BD squared$ Eq2
As AD is median , D is mid point then BC = 2BD
Subtract Eq1 - Eq2
We get, $AC squared minus AD squared equals AB squared plus BC squared minus open parentheses AB squared plus BD squared close parentheses$
$AC squared minus AD squared equals BC squared minus BD squared text substitute end text BC equals 2 BD$
$AC squared minus AD squared equals 4 BD squared minus BD squared$
$AC squared minus AD squared equals 3 BD squared$
Hence proved

Related Questions to study

$ABC text is an equilateral triangle end text. straight K text is a point on end text BC text such that end text BK colon KC equals 2 colon 1 text . Prove that end text 9 AK squared equals 7 AC squared$

$ABC text is an equilateral triangle end text. straight K text is a point on end text BC text such that end text BK colon KC equals 2 colon 1 text . Prove that end text 9 AK squared equals 7 AC squared$

The perpendicular AD on the base BC of Triangle ABC intersects BC in D such that BD = 3CD. Prove that
$2 A B squared equals 2 A C squared plus B C squared$

The perpendicular AD on the base BC of Triangle ABC intersects BC in D such that BD = 3CD. Prove that
$2 A B squared equals 2 A C squared plus B C squared$

In an equilateral $straight triangle ABC text , end text$ the side BC is trisected at D . Prove that $9 A D squared equals 7 A B squared$
.

In an equilateral $straight triangle ABC text , end text$ the side BC is trisected at D . Prove that $9 A D squared equals 7 A B squared$
.

parallel

ABC and DBC are two isosceles triangles on the same base BC. Show
that $straight angle ABD equals straight angle ACD$

ABC and DBC are two isosceles triangles on the same base BC. Show
that $straight angle ABD equals straight angle ACD$

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

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

parallel

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.

$A B C text is a right triangle with end text straight angle A equals 90 to the power of ring operator BL text and end text CM text are its medians. Prove that end text 4 open parentheses BL squared plus CM squared close parentheses equals 5 BC squared text . end text$

$A B C text is a right triangle with end text straight angle A equals 90 to the power of ring operator BL text and end text CM text are its medians. Prove that end text 4 open parentheses BL squared plus CM squared close parentheses equals 5 BC squared text . end text$

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

parallel

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.

$text In Triangle end text A B C text , If end text A D text is the median show that, end text A B squared plus A C squared equals 2 open parentheses A D squared plus B D squared close parentheses$

$text In Triangle end text A B C text , If end text A D text is the median show that, end text A B squared plus A C squared equals 2 open parentheses A D squared plus B D squared close parentheses$

Classify whether the following Surd is rational or irrational , justify 8-√48

Classify whether the following Surd is rational or irrational , justify 8-√48

parallel

Classify whether the following Surd is rational or irrational , Justify.√47+√8

Classify whether the following Surd is rational or irrational , Justify.√47+√8

In the figure, sides QP and RQ of a $straight triangle P R R$ are produced to points S and T respectively.
If $straight angle SPR equals 135 to the power of ring operator$ and $straight angle POT equals 110 to the power of ring operator$ , find $straight angle PRQ$ .

In the figure, sides QP and RQ of a $straight triangle P R R$ are produced to points S and T respectively.
If $straight angle SPR equals 135 to the power of ring operator$ and $straight angle POT equals 110 to the power of ring operator$ , find $straight angle PRQ$ .

Simplify √8 - √18 + √50

Simplify √8 - √18 + √50

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.