Alyssa Z.

asked • 03/20/21

Suppose that RG = 4, GS = 5, SH = 5, and HT = 8.  Find KT/KR

Consider △RST, with point D in the interior.


Suppose that RG = 4, GS = 5, SH = 5, and HT = 8.

 Find KT/KR

.


Brenda D.

tutor
If you could supply a bit more information. Consider △RST, with point D in the interior. Suppose that RG = 4, GS = 5, SH = 5, and HT = 8. The lengths given indicate that the lines in Triangle RST are not Medians since by definition: A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. If point D is the incenter or the circumcenter and you need to find out or determine that then you could have Angle Bisectors. You need to define point D. Again since your lengths would indicate that your lines are not Medians and the Centroid is by definition is a point of concurrency of the triangle. It is the point where all 3 medians intersect and is often described as the triangle's center of gravity or as the barycent. Point D is not a centroid. If you could show that Point D is the circumcenter of Triangle RTS and the lines TG and RH are Perpendicular Bisectors then you could use the Angle Bisector Theorem to find KT/KR
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03/21/21

Brenda D.

tutor
Thanks for the diagram. It does show that RG + GD = RS = 9 and SH + HT = 13. If you can show that you have Triangle Bisectors with an incenter or circumcenter then there are ratios that apply to the triangles created.
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03/21/21

Paul M.

tutor
Alyssa...I would be very grateful if you could make a comment as to how you uploaded the figure. Thank you!
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03/21/21

1 Expert Answer

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Philip P. answered • 03/21/21

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Point D is NOT a circumcenter or centroid or orthocenter, so I suspect it is the incenter. The incenter is the point of concurrency (intersection) of the triangle's three angle bisectors. An angle bisector divides the opposite side into two segments that are proportional to the other two sides of the triangle. So SK divides RT into 2 segments, KT and KR. Hence:


KT/KR = RS/ST


RS = RG + GS = 4 + 5 = 9

ST = SH + HT = 5 + 8 = 13


KT/KR = 9/13

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