JK¯¯¯¯¯¯¯¯, KL¯¯¯¯¯¯¯¯, LJ¯¯¯¯¯¯¯ are all tangent to circle O. The diagram is not drawn to scale. If JA = 15, AL = 18 and CK = 6, what is the perimeter of triangle JKL? (1 point) Responses 64 64 39 39 78 78 32

Answer 1

To find the perimeter of triangle JKL, we need to find the lengths of each side of the triangle.

Since JK¯¯¯¯¯¯¯¯ is tangent to circle O, and JA = 15, then JK¯¯¯¯¯¯¯¯ is the sum of JA and AK (since they are radii of the same circle). Let's find AK first:

AK = AL - LK = 18 - 15 = 3

JK = JA + AK = 15 + 3 = 18

Similarly, since KL¯¯¯¯¯¯¯¯ and LJ¯¯¯¯¯¯¯ are tangent to circle O, and CK = 6, then KL¯¯¯¯¯¯¯¯ and LJ¯¯¯¯¯¯¯ are also the sum of their respective radii. Let's find LJ first:

LJ = LA + AC = 18 + 6 = 24

Similarly, KL¯¯¯¯¯¯¯¯ = 18 + 6 = 24

Now we have the lengths of all three sides of triangle JKL:

JK = 18
KL = 24
LJ = 24

The perimeter of triangle JKL is the sum of all three sides:

Perimeter = JK + KL + LJ = 18 + 24 + 24 = 66

Therefore, the perimeter of triangle JKL is 66.