CInsbstnkng

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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.

CInsbstnkng Apr 20, 2026

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In the diagram below, chords $\overline{AB}$ and $\overline{CD}$ are perpendicular, and meet at $X.$ Find the diameter of the circle.

CInsbstnkng Apr 20, 2026

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Math

A fair coin is tossed repeatedly until either heads comes up three times in a row or tails comes up four times in a row. What is the probability that the coin will be tossed more than 10 times? Express your answer as a common fraction.

CInsbstnkng Oct 7, 2025

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Math

In triangle ABC, cos A=sqrt(7/10) and cos B=sqrt(3/10) Find cos C

CInsbstnkng Oct 7, 2025

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Trapezoid ABCD has bases \overline{AB} and \overline{CD}. The extensions of the two legs of the trapezoid intersect at $P$. If $[PBC] = 15$ and $CD = 3 \cdot AD,$ what is $[ABCD]$?

CInsbstnkng Aug 19, 2025

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Trapezoid ABCD has bases \overline{AB} and \overline{CD}. The extensions of the two legs of the trapezoid intersect at $P$. If $[ABD]=8$ and $[PBC]=8$, then what is $[PAB]$?

CInsbstnkng Aug 19, 2025

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An equilateral triangle, a regular heptagon, a square, a 20-gon, a regular pentagon, a regular hexagon, and a regular n-gon, all with the same side length also completely surround a point. Find n.

CInsbstnkng Aug 18, 2025

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Let ABCDE be an equilateral pentagon. If the pentagon is concave, and $\angle A = \angle B = 90^{\circ},$ then what is the degree measure of $\angle E$?

CInsbstnkng Aug 18, 2025

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Find all ordered pairs x, y of real numbers such that x+y=10 and x^3+y^3=300.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).

CInsbstnkng Aug 17, 2025

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For an integer n, the inequality
x^2 + nx + 15 < -89 - 3x^2
has no real solutions in $x$. Find the number of different possible values of $n$.

CInsbstnkng Aug 17, 2025

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Shown below is rectangle EFGH. Its diagonals meet at Y. Let $X$ be the foot if an altitude is dropped from $E$ to $\overline{FH}$. If EX = 24 and $GY = 30$, find the perimeter of rectangle $EFGH$.

CInsbstnkng Aug 13, 2025