Show that r(r(1)+r(2)+r(3))=ab+bc+ca-s^(...

Show that `r(r_(1)+r_(2)+r_(3))=ab+bc+ca-s^(2).`

Text Solution

Verified by Experts

The correct Answer is:

`ab+bc+ca-s^(2)=R.H.S`

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Show that r_(1)+r_(2)+r_(3)-r=4R

Show that rr_(1)r_(2)r_(3)=Delta^(2)

Knowledge Check

r+r_(3)+r_(1)-r_(2)=

A

`4R cosA`

B

`4R cosB`

C

`4R cosC`

D

4R

a( r r _1 +r_2r_3) =

A

`( ca - r_3r_1) /( r_2)`

B

` ( r_3r- r_1r_2)/( ab ) `

C

` ( r_3^(2))/( 4R-r_1-r_2)`

D

abc

(r_(1)-r)(r_(2)-r)(r_(3)-r)=

A

4Rr

B

4Rs

C

`4R Delta`

D

`4Rr^(2)`

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Show that r r_1 r_2 r_3 = Delta^2

Prove that r(r_1 + r_2 + r_3) = ab + bc + ca- s^2 .

In DeltaABC, " show that " (ab-r_(1)r_(2))/(r_(3))=(bc-r_(2)r_(3))/(r_(1))=(ca-r_(3)r_(1))/(r_(2))

Show that r+r_(3)+r_(1)-r_(2)=4RcosB.

Prove that r+r_(1)+r_(2)-r_(3)=4RcosC

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