`stackrel(harr)(dg)` and `stackrel(harr)(eg)` are tangent to circle c and circle f. the points of tangency are a, b, d, and e. if m`/_dfe` = 140°, what is m`/_acb`?

General Idea:

Sum of angles subtended at the centre and point of contact by tangents down from an external point is supplementary (180°).

Applying the concept:

Considering the point of contact of two tangents of large circle, we can write

We are given , so the equation will become

{Subtracting 140 on both sides}

Considering the point of contact of two tangents of small circle, we can write

Subtracting 40 on both sides, we get...

Conclusion:

none of the option is correct.

step-by-step explanation:

it says to find which expression equals 9^3 sqrt 10 = ?

9^3 sqrt 10 = 729 sqrt 10.

checking option a. 5 sqrt 10 + 4 sqrt 10

5 sqrt 10 + 4 sqrt 10

= 9 sqrt 10.

checking option b. 5^3 sqrt 10 + 4^3 sqrt 10

5^3 sqrt 10 + 4^3 sqrt 10

= 125 sqrt 10 + 64 sqrt 10

= 189 sqrt 10.

checking option c. 5 sqrt 10 + 4^3 sqrt 10

5 sqrt 10 + 4^3 sqrt 10

= 5 sqrt 10 + 64 sqrt 10

= 69 sqrt 10.

checking option d. 5^3 sqrt 10 + 4 sqrt 10

5^3 sqrt 10 + 4 sqrt 10

= 125 sqrt 10 + 4 sqrt 10

= 129 sqrt 10.

hence, none of the option is correct.

the solution is 12x-6y