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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.

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 un class=

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mhanifa

Answer:

  • 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

The perimeter of given triangle is 20 units.

What is a two tangent theorem?

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

Solution:-

PJ = PG, HF = HJ, and EF = EG.

Given that EF = 10, EG must also be 10 units.

Triangle EHP's exterior is bounded by:

P = EH, HP, and EP.

We could use instead:

HP is the segment addition of HJ and PJ, where HJ and PJ each have an HF and PG value.

The perimeter is then:

P = (EH + HF) + (EP + PJ)

EF + EG = 10 + 10 = 20

To know more about perimeter visit:-

brainly.com/question/6465134

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