Question

10.

J
A
B
0
L
с
K
Not drawn to scale
JK, KL, and are all tangent to circle O. JA = 9, AL = 10, and CK = 14. What is the perimeter of AJKL?
66 units
46 units
O 33 units
38 units

Answer 1

66

Explanation:

The figure of triangle JKL is attached. JA = 9, AL = 10, and CK = 14.

According to two tangent theorem, the tangent to a circle that meets at the same point is equal to each other. Therefore:

AJ = BJ, AL = CL, CK = BK.

Since AJ = 9, BJ = AJ = 9

AL = 10, CL = AL = 10

CK = 14, BK = CK = 14.

Therefore the lengths of the triangle sides are:

JL = AJ + AL = 9 + 10 = 19

JK = BJ + BK = 9 + 14 = 23

KL = CL + CK = 14 + 10 = 24

The perimeter of the triangle is the sum of all its sides, it is given as:

Perimeter = JL + JK + KL = 19 + 23 + 24 = 66