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

Conclusion of egroff''s theorem and lusin''s theorem, (1) Show that the con...

(1) Show that the conclusion of Egroff's theorem can fail if the measure of the domain E is not finite. (2) Extend the Lusin's Theorem to the case when the measure of the domain E

Algebra, what is the answers of exercise 3.1

what is the answers of exercise 3.1

The expected monetary value method, The expected monetary value method ...

The expected monetary value method The expected pay off as profit associated with a described combination of act and event is acquired by multiplying the pay off for that act a

Relation between hieght, volume=(1/3)(pi)(radius of base)2(height) curved ...

volume=(1/3)(pi)(radius of base)2(height) curved surface area=(pi)(r)(l), r is radius of base and l is length of straight line connecting apex of cone with point on edge of base

Velocity of derivation, Velocity : Recall that it can be thought of as sp...

Velocity : Recall that it can be thought of as special case of the rate of change interpretation. If the situation of an object is specified by f(t ) after t units of time the vel

Function evalaution, how do we solve function evaluation f(x)

how do we solve function evaluation f(x)

6thgrade, do you have 3 digit and 4 digit number problem

do you have 3 digit and 4 digit number problem

Parameters of the poisson mixture model, Using R function nlm and your code...

Using R function nlm and your code from Exercise E1.2, write an R function called pois.mix.mle to obtain MLEs of the parameters of the Poisson mixture model.

Prove that prims algorithm produces a minimum spanning tree, Prove that Pri...

Prove that Prim's algorithm produces a minimum spanning tree of a connected weighted graph. Ans: Suppose G be a connected, weighted graph. At each iteration of Prim's algorithm

Transpose of a matrix, I didn't understand the concept of Transpose of a Ma...

I didn't understand the concept of Transpose of a Matrix, need assistance.

Write Your Message!

Name

Email id

Message

Verfication Code

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!

Submit Assignment

User Account

All Pages