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 dividing fractions, What is Dividing Fractions? If you want to ...

What is Dividing Fractions? If you want to divide two fractions, you invert the second fraction (that is, turn it upside-down) and change the division sign to a multiplication

Proof of: limq -0 sinq/q = 1 trig limits, Proof of: lim q →0 sin q...

Proof of: lim q →0 sin q / q = 1 This proofs of given limit uses the Squeeze Theorem. Though, getting things set up to utilize the Squeeze Theorem can be a somewha

Proof of various derivative facts formulas properties, PROOF OF VARIOUS DER...

PROOF OF VARIOUS DERIVATIVE FACTS/FORMULAS/PROPERTIES Under this section we are going to prove several of the different derivative facts, formulas or/and properties which we en

Math, weather prediction on monsoon past data on project

weather prediction on monsoon past data on project

Dividing fractions by fractions with drawing.., how do I divide a fraction ...

how do I divide a fraction by a fraction by drawing a picture

#t, show that a*0=a

show that a*0=a

How much do they save if they pay the bill inside 10 days, Oscar's Oil Comp...

Oscar's Oil Company provides customers a 5% discount if they pay their bill within 10 days. The Stevens' oil bill is $178. How much do they save if they pay the bill inside 10 days

Find poq of tangents drawn to the circle, In figure, O is the centre of th...

In figure, O is the centre of the Circle .AP and AQ two tangents drawn to the circle. B is a point on the tangent QA and ∠ PAB = 125 ° , Find ∠ POQ. (Ans: 125 o ) An s:

Money, how do you add 1,ooo and 100?

how do you add 1,ooo and 100?

Solutions to systems, Now that we've found some of the fundamentals out of ...

Now that we've found some of the fundamentals out of the way for systems of differential equations it's time to start thinking about how to solve a system of differential equations

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