Question

Given: Circles k1(A) and k2(O)ext. tangent KE - tangent to k1(A) and k2(O) AK=5, OE=4 Find: KE

Answer 1

Answer:

Step-by-step explanation:

Given

Radius of the circle k1(A) = KA and AX=5

Radius of the circle k2(O) = OE and XO=4

Distance between two center = $AO= AX+XO=5+4=9$

Distance between $AM=AK-OE=5-4=1$

In right angled triangle AOM,

AO=9 and AM=1

Therefore,

$MO=\sqrt{(AO)^{2}-(AM)^{2}}\\\\\Rightarrow MO=\sqrt{(9)^{2}-(1)^{2}}\\\\\Rightarrow MO=\sqrt{(81-1)}\\\\\Rightarrow MO=\sqrt{80}\\\\\Rightarrow MO=2\sqrt{20}$

AS $MO=KE=2\sqrt{20}$