Find the value of X in the following diagram. Here, B and D are points of tangency.

Theorem: Tangent segments from the same external point are congruent
So the two expressions you can set equal to each other

3x+10= 7x-6
-3x -3x

10= 4x-6
+6 +6

16= 4x

X=4

1.   an exact solution requires a radical solution - no decimal approximation.2. (a)4x^3 = 756x^3 = 756/4 = 189x =   cube root of 189 =   5.74   to nearest hundredth answer(b)   189 = 3*3*3*7   so we can write the cube root of 189 as 3∛7 answerchecking (a) 4*(5.74^3 =   756.48   which is very close(b)   4* ((3∛3)^3   = 4*189   = 756   - spot on! 3. i would use solution b because the original question asked for an exact solution.