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

Tangents with parametric equations - polar coordinates, Tangents with Param...

Tangents with Parametric Equations In this part we want to find out the tangent lines to the parametric equations given by X= f (t) Y = g (t) To do this let's first r

Algebra, sir/madam, i abdulla working as a maths teacher want to join ur es...

sir/madam, i abdulla working as a maths teacher want to join ur esteemed organisation as a tutor how can i proceed i have created an account even pls guide me, thanks abdulla

Shares and divident, A man invest ?13500 partly in shares paying 6% at ?140...

A man invest ?13500 partly in shares paying 6% at ?140 and partly in 5% at 125.If he is tolal income is 560, how much has he invested in each?

Indices, 16 raised to the power x eqaual to x raised to the power 2. find x...

16 raised to the power x eqaual to x raised to the power 2. find x

Number line, I need to graph rational numbers on the number line Point A-.6...

I need to graph rational numbers on the number line Point A-.60, point B-1/4, point C-.4,point D-7/8

Divison, what is 24 diveded by 3

what is 24 diveded by 3

Continuity, give me some examples on continuity

give me some examples on continuity

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

Compute projection scale factor, 1. A survey line on campus is measured to ...

1. A survey line on campus is measured to be 1000.00 ft long on horizontal ground. The elevation of the line is 700.00 feet and the geoid separation from ellipsoid to geoid is -110

Integration and differentiation, Integration and Differentiation Diffe...

Integration and Differentiation Differentiation deals along with the determination of the rates of change of business activities or merely the process of finding the derivativ

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