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The perimeter of triangle ABC is 106 cm. Points J,F, and H are points of tangency. What is the value of x in the diagram

The perimeter of triangle ABC is 106 cm. Points J,F, and H are points of tangency-example-1
User Tejinder
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1 Answer

6 votes

Answer:

x = 11

Explanation:

If there are two tangent lines to a circle, departing from the same point, the tangent lines have the same length.

So, as FB and HB are tangent lines to the circle, and both depart from point B, we have that FB = HB.

In the same way, we have that FA = AJ and JC = CH.

If the perimeter of the triangle is 106, we have that:

FB + FA + AJ + JC + CH + HB = 106

x + 5 + 15 + 15 + 2x + 2x + x + 5 = 106

6x + 40 = 106

6x = 66

x = 11

User TuomasK
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