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

What is the sample space for this experiment, A die is thrown repeatedly un...

A die is thrown repeatedly until a six comes up. What is the sample space for this experiment? HINT ;A= {6} B={1,2,3,4,5,} Ans: The sample space is = {A, BA, BBA, BBBA, BBBBA.

Trigonomitry, Ask if tanA+sinA=m and m^2-n^2=4 rute mn show that tanA-sinA=...

Ask if tanA+sinA=m and m^2-n^2=4 rute mn show that tanA-sinA=n

Draw tangent graph y = sec ( x ), G raph y = sec ( x ) Solution: As wi...

G raph y = sec ( x ) Solution: As with tangent we will have to avoid x's for which cosine is zero (recall that sec x =1/ cos x) Secant will not present at

Linear equation, tens digit of a 2-digit number is twice its unit digit. If...

tens digit of a 2-digit number is twice its unit digit. If the sum of the digit is 12, find the number.

Algebra, 25 algebraic equations that equal 36

25 algebraic equations that equal 36

Geometry, how do we rotate an object 90 counterclockwise?

how do we rotate an object 90 counterclockwise?

Volume and surface area, a conical hole drilled in a circular cylinder of h...

a conical hole drilled in a circular cylinder of height 12 and radius 5cm the height and radius of cone are also same find volume

Linear probability model, Pepsi:               A dummy variable where 1 den...

Pepsi:               A dummy variable where 1 denotes choice of Pepsi by the i-th customer and 0 otherwise Price_P:           The price of a 2-liter bottle of Pepsi at the time

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