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 D is on side AC of 4ABC. We know [ABC] = 120, AD = 8, DC = 4. What is [ABD]?

In the diagram, 4ABC ∼ 4ACD. If AD = 12 and DB = 15, what is AC?

O is the circumcenter of 4ABC. If OB = OC = BC, what is ∠BAC?

In the diagram, ∠ABC = ∠BDC = 90◦ . We know BD = 30 and CD = 72. What is AB?

H is the orthocenter of 4ABC. We know AB = AC = BC/ √ 3. What is ∠BHC?

E is a point on side CD of square ABCD. The extensions of AD and BE intersect at F. [DEF] = 8 and [ECB] = 18. Find [ABCD].

CD and EF are parallel to AB. They divide the area of 4PAB into three equal parts. If PE = 1, what is AC?

A right isosceles triangle is a triangle with two sides that are equal in length and are perpendicular to each other. The medial triangle of 4ABC is the triangle whose vertices are the midpoints of the sides of 4ABC. Prove that the medial triangle of a right isosceles triangle is also a right isosceles triangle.

Line segments AB and CD intersect at P such that AP = CP and BP = DP. We can then conclude 4BDA  4 . Prove your conclusion

In 4SPT, Q is on SP and R is on PT. We know PQ = 8, QS = 4, ST = 9, and PR = QR = 6. Find all possible values of RT.

I and G are the incenter and centroid of 4ABC. We know AB = 5, AC = 11, and IG k BC. What is BC?

 Dec 3, 2020
 #1
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Q: D is on side AC of 4ABC. We know [ABC] = 120, AD = 8, DC = 4. What is [ABD]?

 

A: [ABD] = 65.

 

Q: In the diagram, 4ABC ∼ 4ACD. If AD = 12 and DB = 15, what is AC?

 

A: AC = 18.

 Dec 3, 2020
 #2
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thanks!

gomgu111  Dec 3, 2020
 #3
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D is on side AC of 4ABC. We know [ABC] = 120, AD = 8, DC = 4. What is [ABD]?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 [ABC] = 120           AD = 8              DC = 4

 

Let the height of ΔABC be BD

 

BD = 2[ABC] / AC  ==>     BD = 20 units

 

[ABD] = 1/2 (AD * BD)  ==>     [ABD] = 80 u2

Guest Dec 3, 2020
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lol this is aops test its easy dont worry

Guest Dec 12, 2020

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