Two circles of radii a-and-b -a-b- touch each other externally- ST is a common tangent touching the circles S and T respectively- then ST-2 is equal toa-bab2ab4ab

Question

Toppr Admin · Accepted Answer

Take a line parallel to AB with an end at T-CT-x2225-AB-AB-a-b-CS-a-x2212-b-WKT -x2220-AST-90-In -x25B3-CST-CS2-CT2-ST2-x27F9-ST2-a-b-2-a-x2013-b-2-2ab-x2013-x2212-2ab-4ab-xA0-

Two circles of radii $a a n d b$ $(a > b)$ touch each other externally. $S T$ is a common tangent touching the circles at $S$ and $T$ respectively, then $S T^{2}$ is equal to

$a + b$
$a b$
$2 a b$
$4 a b$

Take a line parallel to AB with an end at T

$C T ∥ A B$

$A B = a + b$

$C S = a - b$

WKT $∠ A S T = 90$

In $△ C S T$

$C S^{2} + C T^{2} = S T^{2}$

$⟹ S T^{2} = (a + b)^{2} + (a - b)^{2} = 2 a b - (- 2 a b) = 4 a b$

Two circles of radii aandb (a>b) touch each other externally. ST is a common tangent touching the circles at S and T respectively, then ST2 is equal toa+bab2ab4ab

Take a line parallel to AB with an end at T CT∥AB AB=a+b CS=a−b WKT ∠AST=90 In △CST CS2+CT2=ST2 ⟹ST2=(a+b)2+(a–b)2=2ab–(−2ab)=4ab

Two circles of radii $a a n d b$ $(a > b)$ touch each other externally. $S T$ is a common tangent touching the circles at $S$ and $T$ respectively, then $S T^{2}$ is equal to

$a + b$
$a b$
$2 a b$
$4 a b$

Take a line parallel to AB with an end at T

$C T ∥ A B$

$A B = a + b$

$C S = a - b$

WKT $∠ A S T = 90$

In $△ C S T$

$C S^{2} + C T^{2} = S T^{2}$

$⟹ S T^{2} = (a + b)^{2} + (a - b)^{2} = 2 a b - (- 2 a b) = 4 a b$