BlackoutMiIkshake

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In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 12$, find $BC$.

BlackoutMiIkshake Apr 7, 2026

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In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $BC = 15,$ and $CX = 5$. What is $BX$?

BlackoutMiIkshake Apr 7, 2026

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Alex chooses a number at random from the set {1, 2, 3, 4, 5}. Winnie also chooses a number at random from the same set. (They can choose the same number.) What is the probability that the product of their numbers is at least 4? read more ..

BlackoutMiIkshake Apr 7, 2026

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In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?

BlackoutMiIkshake Apr 7, 2026

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Let ABC be a triangle with \angle B = 90^{\circ}. Suppose that point D lies on segment BC such that angle BAD = \angle CAD, and suppose that point E lies on segment AC such that angle EDA = 60^{\circ}. Given that AD = AC and that CE = 17, find BD.
<read more ..

BlackoutMiIkshake Apr 7, 2026

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help geometry

In the diagram below, AB = AC = 1, and arc BC is centered at A with \angle BAC = 60^\circ. Point D is on \overline{AB}, and point E is on arc BC so that BD = DE, and arc BE (centered at D) is tangent to \overline{AC}. Point F is on \overline{DB}, read more ..

BlackoutMiIkshake Apr 7, 2026

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Siva starts at vertex A of square ABCD with side length 10. He walks towards vertex C, along the diagonal AC. He then walks towards B, then towards D. What is the length of his path?

BlackoutMiIkshake Apr 7, 2026

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help geo

In triangle ABC, let D be a point on side BC. Select all the true statements.
If AD is an altitude of triangle ABC, then AC > AD.
If AD is a median of triangle ABC, then BD > CD.
If AD is an angle bisector read more ..

BlackoutMiIkshake Apr 7, 2026

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In triangle $XYZ,$ circles are drawn centered at $X$, $Y$, and $Z$, so that all pairs of circles are externally tangent. If $XY = 2,$ $XZ = 2,$ and $YZ = 2$, then find the sum of the areas of all three circles.

BlackoutMiIkshake Apr 6, 2026

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In equiangular octagaon EFGHIJKL, we know that EF = GH = IJ = KL = 1 and FG = HI = JK = LE = sqrt(2). Find the area of the octagon.

BlackoutMiIkshake Apr 6, 2026