Question

If a right-angled DABC of maximum area is inscribed within a circle of radius R, then-

• A. D = 2R²
• B. $\frac { 1 } { r _ { 3 } }$=
• C. r = ($\sqrt { 2 }$– 1) R
• D. s = (1 + $\sqrt { 2 }$)R

Answer 1

Answer: (B)

$\frac { 1 } { r _ { 3 } }$=

Answer 2

For a right-angled triangle inscribed in a circle of radius

R, the length of the hypotenuse is 2R. \ the area is maximum

when the triangle is isosceles with each side = $\sqrt { 2 }$R.

\ s = $\frac { 1 } { 2 }$ (2$\sqrt { 2 }$+ 2) R = ($\sqrt { 2 }$+ 1)R

\ D =$\frac { 1 } { 2 }$ $\sqrt { 2 }$R. $\sqrt { 2 }$R = R² ̃ = $\frac { ( \sqrt { 2 } + 1 ) } { R }$

$\frac { 1 } { \mathrm { r } _ { 1 } }$ + + $\frac { 1 } { r _ { 3 } }$= $\frac { \mathrm { s } - \mathrm { a } } { \Delta }$ + + $\frac { \mathrm { s } - \mathrm { c } } { \Delta }$ = $\frac { \mathrm { s } } { \Delta }$ ==