Question

30 POINTS AVAILABLE

For circle K and circle L, Segment J M is a common internal tangent. If JK = 3, LM = 9 and JM = 20, find KL. Show all work.

Answer 1

Explanation:

Triangles JKN MLN are similar.

There is a right angle at J and M. <JNK and <MNL are vertically opposite. By AA the triangles are similar.

Find JN

JK = 3

LM = 9

JK/LM = JN/(20 - JN)

3/9 = JN/(20 - JN)

1/3 = JN/(20 - JN)

20 - JN = 3JN

20 = 4JN

JN = 5

NM = 20 - 5

NM = 15

Find KN

KN^2 = JN^2 + JK^2

JK = 3

JN = 5

KN = ?

KN^2 = JK^2 + JN^2

KN^2 = 3^2 + 5^2

KN^2 = 34

KN = sqrt(34)

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Find LN

LN = ?

MN = 15

LM = 9

LN = sqrt(15^2 + 9^2)

LN = sqrt(306)

LN = 3*sqrt(34)

Find LK

LK = sqrt(34) + 3sqrt(34)

LK = 4 sqrt(34)