MEMEG0D

91 Questions
15 Answers

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Geometry

Point X is on side \overline{AC} of triangle $ABC$ such that $\angle AXB =\angle ABX + 20^\circ$, and $\angle ABC - \angle BAC = 36^\circ$. Find $\angle XBC$ in degrees.

MEMEG0D 6 hours ago

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+380

Geometry

Two angle bisectors of triangle ABC, $\overline {BE}$ and $\overline {CF}$, intersect at $P$. What is $\angle A$ in degrees?

MEMEG0D 6 hours ago

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+380

Geometry

In the diagram, \overline{BE} bisects \angle ABC, and $\overline{CE}$ bisects $\angle ACD.$ Compute $\angle BAC,$ in degrees.

MEMEG0D 6 hours ago

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+380

Geometry

In pentagon ABCDE, \overline{AC} bisects \angle BCE and $\overline{AD}$ bisects $\angle BDE.$ If $\angle CBD = 30^\circ$ and $\angle CED = 60^\circ,$ then find $\angle CAD,$ in degrees.

MEMEG0D 6 hours ago

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+380

Geometry

Two tangents $\overline{PA}$ and $\overline{PB}$ are drawn to a circle, where $P$ lies outside the circle, and $A$ and $B$ lie on the circle. The length of $\overline{AB}$ is $4,$ and the circle has a radius of $5.$ Find the length $AB.$

MEMEG0D 3 janv. 2025

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+380

Geometry

We have a triangle $\triangle ABC$ and a point $K$ on $BC$ such that $AK$ is an altitude to $\triangle ABC$. If $AC = 8,$ $BK = 2$, and $CK = 3,$ then what is $AB$?

MEMEG0D 2 janv. 2025

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+380

Geometry

Altitudes AD and BE of acute triangle ABC intersect at point H. If angle ABH = 30 and angle DAC = 45, then what is angle HCA in degrees?

MEMEG0D 2 janv. 2025

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+380

Geometry

In trapezoid EFGH, \overline{EF} \parallel \overline{GH}, and P is the point on \overline{EH} such that EP:PH = 1:2. If the area of triangle PEF is 6, and the area of triangle PGH is 6, then find the area of trapezoid EFGH.

MEMEG0D 2 janv. 2025

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+380

Algebra

Let x, y, and z be nonzero real numbers. Find all possible values of
(x + y + z)/(|x| + |y| + |z|).

MEMEG0D 1 janv. 2025

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+380

Number Theory

Find the number of bases n \ge 2 such that 100_n + 1_n is prime.

MEMEG0D 1 janv. 2025

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+380

Geometry

A circle is drawn inside triangle ABC, tangent to $\overline{AC},$ $\overline{BC},$ and the semicircle with diameter $\overline{AB}.$ The radius of the circle is $1,$ and $\angle BAC = 60^\circ.$ Find the area of triangle $ABC.$

MEMEG0D 27 déc. 2024