In the diagram, which must be true for point D to be an orthocenter? BE, CF, and AG are angle bisectors. BE ⊥ AC, AG ⊥ BC, and C
F ⊥ AB. BE bisects AC, CF bisects AB, and AG bisects BC. BE is a perpendicular bisector of AC, CF is a perpendicular bisector of AB, and AG is a perpendicular bisector of BC.
2 answers:
BE, CF and AG are angle bisectors. Therefore, their meeting point is I, the incentre of the triangle ABC.
BE ⊥ AC, AG ⊥ BC, and CF ⊥ AB. Therefore, meeting point of BE, CF and AG is O, the orthocentre of the triangle ABC.
BE bisects AC, CF bisects AB, and AG bisects BC. Therefore, BE, CF and AG are medians and their meeting point is G, the centroid of the triangle ABC.
From the above, it is clear that I = O = G.
This property holds good only for equilateral triangles.
Hence, Δ ABC is an equilateral triangle.
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Answer:
Step-by-step explanation:
Let age of each twin be x
let age of sister be s
So we can write:
x + 4 = s
The product of the 3 siblings ages is 3482 more than sum. We can write:
This can be simplified as:
We replace s with "x + 4" and solve:
<u>Note:</u> To solve this cubic, we used technology
Thus, we can say the twins are 14 years old