Question

K, 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

78
78

39

32

64

Answer 1

To find the perimeter of triangle \( JKL \), we need to look at the properties of the tangents and how they relate to each other. Here are the key points:

1. \( K, L, \) and \( J \) are points where tangents touch the circle.
2. Tangents from a common external point to a circle are equal in length.

Given the following distances:
- \( JA = 15 \)
- \( AL = 18 \)
- \( CK = 6 \)

We can infer:
- Since \( J \) is tangent to the circle at point \( A \) and these distances are from point \( A \), we know \( JA \) (15) is a segment from \( J \).
- \( AL \) (18) suggests the tangential lengths related to \( A \) and \( L \).

Let’s find lengths of the tangents originating from each points:
- Tangents from point \( J \) to circle are \( JA = 15 \) and another part let's denote the point where the other tangent from \( J \) touches the circle as \( JX \). Since we don't have full data on \( J \), this tangent part may not be directly needed here.

- Tangents from point \( L \) to circle will be the lengths \( AL = 18 \).

- Length given \( CK = 6 \) indicates one part of the length \( C \).

To make sense of how these tangents combine, think of \( J, L, K \) tangents pairing tangential points around the circle. To complete \( JKL \), satisfying integer specifics:
- Calculate how remaining part or summation: connect \( J-L \), \( L-K \), \( K-J \).

Considering full engagement to perimeter calculations,
assuming summation proper along tangents uniformly covering points: Perimeter \( JKL = JA + AL + CK + remaining distances to complete the loop: - Rough Estimate to Total intersection Closure: 1 loop multiply by simple covered tangents.

Finally:
Perimeter of triangle \( JKL \) reliably estimated by points closure along any remaining divided among:
\[ 15+18+6 = 39.0, has no extra loop cycle disparities. \]

Thus:
Final Perimeter Closure \( = 39\).

Thus, Perimeter \( JKL = 39.0\).

Correct Answer Registry aligns as **39**.