Prove that ac2 = ap2 + 2(1+2)bp2, Mathematics

Assignment Help:

ABC is a right-angled isosceles triangle, right-angled at B. AP, the bisector of ∠BAC, intersects BC at P. Prove that AC2 = AP2 + 2(1+√2)BP2

861_traingle 4.png

Ans:    AC = √2AB (Since AB = BC)

AB/AC = BP/CP (Bisector Theorem)

⇒ CP = √2 BP

AC2 - AP2 = AC2 - (AB2 + BP2)

= AC2 - AB2 - BP2

= BC2 - BP2

= (BP + PC)2 - BP2

= (BP + √2BP)2 - BP2

= 2BP2 + 2√2  BP2

= 2 ( √2 +1) BP2 ⇒ AC2 = AP2 + 2(1+√2)BP2

Proved


Related Discussions:- Prove that ac2 = ap2 + 2(1+2)bp2

Fraction, in a garden 1/8 of the flowers are tulips. 1/4 of the tulips are ...

in a garden 1/8 of the flowers are tulips. 1/4 of the tulips are rd. what fraction of the flowers in the garden are red tulips

Write a procedure to obtain the inverse of a matrix, Write a procedure to o...

Write a procedure to obtain the inverse of an n by n matrix usingGaussian elimination. (You cannot use A - 1 or any of the built-in packages like 'MatrixInverse'.) Output any a

Abstract algebra, How many homomorphism are there from z2 to z3. Zn is grou...

How many homomorphism are there from z2 to z3. Zn is group modulo n

Parallelogram, fig angles of a irregular polygons exterior and interior .

fig angles of a irregular polygons exterior and interior .

Comparison-types of word problems related to subtraction, Comparison - the...

Comparison - the difference between two groups or numbers, namely, how much one is greater than the other, how much more is in one group than in the other. (e.g., if Munna has

Expert , i want to work with you, please guide me

i want to work with you, please guide me

Tower of hanoi, how to create an activity of tower of hanoi

how to create an activity of tower of hanoi

Find final position of point by rotation -translation matric, Question: ...

Question: A point in 3D is first rotated anticlockwise by 45 degrees about x axis,then translated along y axis by 2 units.Find the final position of the point if its initial po

each player selects one of her two remaining chips , Consider the followin...

Consider the following parlor game to be played between two players. Each player begins with three chips: one red, one white, and one blue. Each chip can be used only once. To beg

Show that 571 is a prime number, Show that 571 is a prime number. Ans: ...

Show that 571 is a prime number. Ans:    Let x=571⇒√x=√571 Now 571 lies between the perfect squares of  (23)2 and (24)2 Prime numbers less than 24 are 2,3,5,7,11,13,17,1

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd