📐 geometry

1. **Problem statement:** We have a circle with two tangent lines from point K touching the circle at points J and L. The angle between the two tangents at K is 81°.

1. **Problem statement:** We have a circle with two tangent lines from point K touching the circle at points J and L. The angle between the two tangents at K is 81°.

1. **State the problem:** We need to find the measure of the minor arc JK in a circle where chords JK and NM intersect at the center L. 2. **Given information:**

1. **State the problem:** We are given a circle with two chords intersecting at point L inside the circle. The angles and arcs are labeled as follows: - Angle at L between rays LJ

1. **Problem statement:** Given a pyramid with a rectangular base of sides $a=6$ cm and $b=4$ cm, and a height $h=5$ cm. The apex is directly above the intersection of the diagonal

1. **Énoncé du problème** : Déterminer l'équation cartésienne de la sphère (S) de centre $\Omega(1,-3,2)$ et de rayon $R=3$.

1. مسئله: خروج از مرکز یک بیضی برابر $\frac{\sqrt{7}}{2}$ و طول قطر کوچک آن 10 است. فاصله کانونی بیضی را بیابید. 2. فرمول‌ها و تعاریف مهم:

1. مسئله: معادله دایره‌ای را بیابید که مرکز آن در نقطه $(1,2)$ باشد و بر خط $1 = 4y - 3x$ مماس باشد. 2. فرمول معادله دایره با مرکز $(h,k)$ و شعاع $r$ به صورت زیر است:

1. **Stating the problem:** We have two triangles, ABC and CDE, which are similar by the given angle conditions: \(\angle B = \angle D\) and \(\angle A = \angle E\). Given side len

1. **State the problem:** We are given a circle with points B, E, and A, and an angle at point A, $\angle BAC = 74^\circ$. We need to find the measure of $\angle BEA$. 2. **Identif

1. **State the problem:** We have a donut with an outer radius of 15 cm and a hole with a diameter of 10 cm (thus radius 5 cm). A bite with diameter 5 cm (radius 2.5 cm) was taken.

1. **Stating the problem:** We are given surface area, volume, and base area values for two shapes: a cylinder and a triangular prism.

1. **State the problem:** We are given a pyramid with base edge length $5$ ft and slant height $13$ ft. We need to find the lateral area, surface area, and volume.

1. **State the problem:** Find the total surface area of a rectangular prism with dimensions 14 in. by 3 in. by 3 in. 2. **Formula:** Surface Area $= 2(lw + lh + wh)$ where $l$, $w

1. **State the problem:** We need to find the total surface area of a rectangular prism-like box with dimensions 14 in. (height), 3 in. (width), and 3 in. (depth). 2. **Formula for

1. **State the problem:** We need to graph the image of rectangle KLMN after reflecting it over the y-axis. 2. **Recall the reflection rule:** When reflecting a point $(x,y)$ over

1. **State the problem:** We need to graph the image of triangle \(\triangle FGH\) after reflecting it over the x-axis. 2. **Given points:** \(F(4, -10)\), \(G(7, -10)\), \(H(5, -6

1. **State the problem:** We need to graph the image of rectangle JKLM after reflecting it over the y-axis. 2. **Recall the reflection rule:** Reflecting a point $(x,y)$ over the y

1. **State the problem:** We need to graph the image of rectangle JKLM after reflecting it over the y-axis. 2. **Reflection over the y-axis rule:** When a point $(x,y)$ is reflecte

1. **State the problem:** We need to graph the image of triangle \(\triangle RST\) after reflecting it over the x-axis. 2. **Reflection over the x-axis rule:** When a point \((x,y)

1. **State the problem:** We need to graph the image of square EFGH after reflecting it over the y-axis. 2. **Reflection rule:** When reflecting a point $(x,y)$ over the y-axis, th