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What conditions would be enough to prove that P is the circumcenter of HJK ?

What Conditions Would Be Enough To Prove That P Is The Circumcenter Of HJK class=

Sagot :

paarya184

Answer:

Option A and C

Step-by-step explanation:

Explanation for why I choose option A :-

If you look at the triangle, HK has a midpoint of point L, HJ has a midpoint of point M, and KJ has a midpoint of point N. Now if you stretch the lines inside of the triangle, they intersect at point P which is known as the circumcenter of HJK, true.

Explanation for why I choose option C :-

Now let us look at the lines stretch inside of the triangle. There are three lines which are congruent. Those lines are PK, HP, and PJ (they are the big lines inside the triangle) are congruent. Since those three line intersect at point P, it make the statement true that P is the circumcenter of HJK.

  • Why option B is not an answer?

We do not know the third line (PN) measurements to find that if the three lines (PL, PM, and PN) are congruent and equal 90⁰. Since we do not know, it would not prove that they are congruent and P is the circumcenter of HJK.

  • Why option D is not an answer?

Well it says that triangle HJK is an acute triangle which is true, but this doesn't prove that P is the circumcenter of HJK.

I hope this helps, thank you :) !!

The required conditions are L, M, N are the midpoints of [tex]\overline{HK}, \overline{HJ}, \overline{KJ}[/tex] and [tex]\overline{PK}\cong \overline{HP}\cong \overline{PJ}[/tex]. So, options A and C are correct.

Given:

The given figure of a triangle HJK.

To find:

The conditions that would be enough to prove that P is the circumcenter of HJK.

Explanation:

The circumcenter of a triangle is the intersection of perpendicular bisectors and it is equidistant from each vertex of the triangle.

P is the circumcenter of triangle HJK if PL, PM, PN are perpendicular bisectors and P is equidistant from vertices H, J, K.

PL, PM, PN are perpendicular bisectors if L, M, N are the midpoints of [tex]\overline{HK}, \overline{HJ}, \overline{KJ}[/tex].

P is equidistant from vertices H, J, K if [tex]\overline{PK}\cong \overline{HP}\cong \overline{PJ}[/tex].

The required conditions are L, M, N are the midpoints of [tex]\overline{HK}, \overline{HJ}, \overline{KJ}[/tex] and [tex]\overline{PK}\cong \overline{HP}\cong \overline{PJ}[/tex]. So, options A and C are correct, and other two options are incorrect.

Learn more:

https://brainly.com/question/10508382

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