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:

2√20

Step-by-step explanation:

 Radius of K1A = KA also AX = 5

Radius of K2O = EO and OX = 4

Distance between two centre = AO = AX + OX

                                      5 + 4 = 9

Distance between AM = AK – OE = 5 – 4 = 1

In right angled triangle AOM, AO = 9 and AM = 1

OM = √OA^2 – AM ^2 = √9^2 – 2^2

OM = √81 – 1

OM = √80

OM = √4 x 20

OM = 2√20

SO OM = KE = 2√20