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

Area of a parallelogram x what is the height in terms of x, The area of a p...

The area of a parallelogram is x 8 . If the base is x 4 , what is the height in terms of x? Since the area of a parallelogram is A = base times height, then the area divided by

Explain factor by grouping, Explain Factor by Grouping ? Factoring by g...

Explain Factor by Grouping ? Factoring by grouping is often a good way to factor polynomials of 4 terms or more. (Sometimes it isn't. It doesn't always work. But it's worth try

Logics Puzzle, It’s been a busy weekend for Larry. Five people in his neigh...

It’s been a busy weekend for Larry. Five people in his neighborhood left on vacation Saturday morning and each of them left a pet for Larry to care for until they return. It’s a go

Classify quadrilaterals, which quadrilaterals have only 1 pair of parallel ...

which quadrilaterals have only 1 pair of parallel sides

How many hours will it take for them to be 822 miles apart, Two trains leav...

Two trains leave the same city at the same time, one going east and the other going west. If one train is traveling at 65 mph and the other at 72 mph, how many hours will it take f

Value of perfect information, Value of perfect information This relates...

Value of perfect information This relates to the amount that we would pay for an item of information such would enable us to forecast the exact conditions of the market and act

Fractions, Mr. And Mrs. samuel visited Florida and purchased 120 oranges. ...

Mr. And Mrs. samuel visited Florida and purchased 120 oranges. They gave 1/4 of them to relatives, ate 1/12 of them in the hotel, and gave 1/3 of them to friends. The shipped the

List some maths activities-tasks-exercises for children, List some activiti...

List some activities/tasks/exercises that you would give a class of 50 children to do to make them aware about patterns, and to articulate what the patterns are. You must be won

VAM, applications of VAM.

applications of VAM.

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