Question

In the figure shown, EF is tangent to the circle at F, and EG is

tangent to the circle at G. Line segments HF, PG, HJ, and PJ
are also tangent segments.
When mEF = 10 units, what is the perimeter of triangle EHP?
Explain your reasoning.

Answer 1

• The perimeter is 20 units

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According to the two-tangent theorem, two tangent segments drawn to one circle from the same external point are congruent.

That is:

• EF = EG,
• HF = HJ,
• PJ = PG.

We have EF = 10 units, it means EG is also 10 units.

The perimeter of triangle EHP is:

• P = EH + HP + EP

We can substitute:

• HP = HJ + PJ, segment addition,
• HJ = HF, stated above,
• PJ = PG, stated above.

Then the perimeter is:

• P = (EH + HF) + (EP + PJ) = EF + EG = 10 + 10 = 20 units