Question

"JK, KL, and JL are all tangents to circle O. If JA=8, AL=13, and CK=11, what is the perimeter of triangle JKL? ill draw the diagram

please help!"

Answer 1

⇒ Perimeter of the ΔJKL = 64 units

Explanation:

Given that : JK, KL, and JL are all tangents to circle O

Now, Tangents drawn to the circle from the same external point are equal to each other

⇒ AL = CL

Since, AL = 13 units

⇒ CL = 13 units

Also, CK = BK = 11 units

And, JA = JB = 8 units

Now, Perimeter of the ΔJKL = JA + AL + CL + CK + BK + JB

⇒ Perimeter of the ΔJKL = 8 + 13 + 13 + 11 + 11 + 8

⇒ Perimeter of the ΔJKL = 64 units

Answer 2

To find the perimeter of the triangle, you must find the values of all sides of the triangle. That would be JL, LK and JK.

JL = JA + AL = 8 + 13 = 21

LK = LC + CK, LC is unknown. However, from the diagram, LK is tangent to the circle at point C, which is situated at the center of LK. This means that LC = CK. With that, we can find LK.

LK = 11 + 11 = 22

Lastly, we find JK. Notice that JK is tangent to the circle at point B and ends in point K. Similarly, JL is tangent to the circle at point A and ends at point L. Point A and B lies on the same level on the x-axis. Same is true with L and K. Therefore, they must have the same length. So, JL = JK = 21

Finally, we sum all sides to obtain the parameter:

P = JL + JK + LK = 21 + 21 + 22 = 64

Thus, the perimeter of triangle JKL is 64 units.