falafronk

94 Questions
0 Answers

0

46

0

+359

Prism

Let $ABCDEFGH$ be a rectangular prism. Find the volume of pyramid $CFAH$.

falafronk Mar 25, 2024

0

27

0

+359

Square

In square ABCD, P is on BC such that BP = 4 and PC = 1, and Q is on line CD such that DQ = 2 and QC = 3. Find sin angle PAQ.

falafronk Mar 25, 2024

0

27

2

+359

Square

A square is inscribed in a right triangle, as shown below. The legs of the triangle are 1 and 3. Find the area of the square.

falafronk Mar 25, 2024

0

33

0

+359

Geometry

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

falafronk Mar 25, 2024

0

23

0

+359

Geometry

In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.

falafronk Mar 25, 2024

+1

28

1

+359

Geometry

Triangle DEF is equilateral. Find AE.

DA = 3, AF = 2

falafronk Mar 25, 2024

+1

37

0

+359

Triangle

In triangle ABC, point X is on side BC such that AX = 10, BC = 10, CX = 5, and the circumcircles of traingles ABX and ACX have the same radius. Find the area of triangle ABC.

falafronk Mar 25, 2024

-1

32

0

+359

Circle

A circle lies inside a quarter-circle, as shown below. The circle is tangent to side $\overline{AO}$ and arc $AB.$ Find the radius of the circle.

falafronk Mar 25, 2024

-1

30

0

+359

triangle

In triangle PQR, M is the midpoint of PQ. Let X be the point on QR such that PX bisects angle QPR, and let the perpendicular bisector of PQ intersect AX at Y. If PQ = 36, PR = 22, QR = 26, and MY = 8, then find the area of triangle PQR

falafronk Mar 25, 2024

-1

22

0

+359

Geometry

In triangle $ABC,$ $\angle C = 90^\circ.$ A semicircle is constructed along side $\overline{AC}$ that is tangent to $\overline{BC}$ and $\overline{AB}.$ If the radius of the semicircle is equal to $1$ and $BC = \sqrt{3}$, then find $AB$. read more ..

falafronk Mar 25, 2024