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

Distinct roots, There actually isn't a whole lot to do throughout this case...

There actually isn't a whole lot to do throughout this case.  We'll find two solutions which will form a basic set of solutions and therefore our general solution will be as,

Slope, One of the more significant ideas that we'll be discussing in this s...

One of the more significant ideas that we'll be discussing in this section is slope. The slope of a line is a measure of the steepness of any particular line and it can also be uti

Area under curve, w/ You could use this sample code to test your C function...

w/ You could use this sample code to test your C functions // Please make appropriate changes to use this for C++. // Following main function contains 3 representative test cases

Definition of limit, Definition of limit : Consider that the limit of f(x)...

Definition of limit : Consider that the limit of f(x) is L as x approaches a & write this as provided we can make f(x) as close to L as we desire for all x adequately clos

Integerts, how do u add and subtract integers

how do u add and subtract integers

Show basic trigonometric functions, Q. Show basic Trigonometric Functions? ...

Q. Show basic Trigonometric Functions? Ans. There are six trigonometric functions and they can be defined using a right angle triangle. We first label each side according

Properties of integer exponents, Note that there are two possible forms for...

Note that there are two possible forms for the third property. Usually which form you use is based upon the form you want the answer to be in. Note as well that several of these

Math help, I need help with direct variation between x and y

I need help with direct variation between x and y

Michael has 16 cds how many cds does kathleen have, Michael has 16 CDs. Th...

Michael has 16 CDs. This is four more than twice the amount that Kathleen has. How many CDs does Kathleen have? Let x = the number of CDs Kathleen has. Four more than twice th

Explain the vertex formula, Explain the Vertex Formula ? The vertex for...

Explain the Vertex Formula ? The vertex formula is a convenient way of finding the vertex of the graph for any quadratic function. The graph of the quadratic equation f(x) = ax

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