Question

A circle is shown. Secants E G and D G intersect at point G outside of the circle. Secant E G intersects the circle at point F and secant D G intersects the circle at point H. The length of E F is x, the length of F G is 6, the length of D H is x + 3, and the length of H G is 5. What is the length of line segment DG? 4 units 7 units 12 units 23 units

Answer 1

The correct answer is C. 12

Explanation:

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Answer 2

Explanation:

The formula we need here is

`6(6+x)=5(5+x+3)`

which simplifies to

`6(6+x)=5(8+x)`

which simplifies to

36 + 6x = 40 + 5x and

x = 4

So DG = 5 + 4 + 3 which is 12