Question

please help

Answer 1

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Answer 2

So for 21, the theorem is that when two chords intersect inside of a circle, the products of the two segments on one of the chords is congruent to the product of the segments oof the other chord. This means that 6 times 3 is equal to 2x. That is that same as 18 = 2x. Therefore, x=9.
For 22, when two sectants intersect outside of a circle, the formula is that the outside portion of a sectant multiplied by the full length of the same segment is equal to the same on the other sectant. It'll be easier to show a specific example. For 22, 6 multiplied by (6+8) equals 4 multiplied by (4 + x). This is the same as 6 times 14 = 4 times (4 + x). 6 times 14 equals 84, so 84 = 4 times (4 + x). 4 times (4 + x) equals 16 + 4x . Then you put that together to be 84 = 16 + 4x. You can subtract 16 from both sides to get 68 = 4x. If you divide both sides by 4, you get 17 = x. In equations, this would be; 6(6+8)=4(4+x) then 6(14)=4(4+x) then 6(14)=16+4x then 84=16+4x then 68=4x then 17=x.
For 23, when a tangent intersects a sectant outside of the circle, you need to square the tangent length and that will be equal to the product of the outside section of the sectant and the entire length of the sectant. So for 23, x squared = (4 times 9). Therefore, x squared = 36. Then you would find the square root of both sides, and the square root of 36 is equal to 6, so x=6.
I hope that helped!!