To solve for y, we first need to find the length of segment BD.
Since segment CB is tangent to the circle, it is perpendicular to the radius at the point of tangency. This means that triangle CBD is a right triangle.
We can use the Pythagorean Theorem to find the length of BD:
BD^2 + CD^2 = BC^2
BD^2 + y^2 = 7^2
BD^2 + y^2 = 49
Since triangle CBD is a right triangle, we can also find the length of BD using the Pythagorean Theorem:
BD^2 + 6^2 = 7^2
BD^2 + 36 = 49
BD^2 = 49 - 36
BD^2 = 13
BD = sqrt(13)
Now we have:
13 = sqrt(13) + y = sqrt(49 - y^2) + y
13 = sqrt(13) + y = sqrt(49 - y^2) + y
13 = 3.61 + y = sqrt(49 - y^2) + y
9.39 = sqrt(49 - y^2)
9.39^2 = 49 - y^2
88.1521 = 49 - y^2
88.1521 - 49 = 49 - 49 - y^2
39.1521 = - y^2
-39.1521 = y^2
sqrt(-39.1521) = sqrt(-1) * sqrt(39.1521)
y = 6.26i
Therefore, the length of segment CD is approximately 6.26 units.
. Segment CB is tangent to the circle, and has a length of 7. The circle has a radius of 6. Solve for y, the length of segment CD.
*
13.9 units
9.22 units
6 units
3.22 units
1 answer
1 answer