📐 geometry

1. **Problem statement:** Three rods k, l, and m of equal length are fixed at a common point. Rods k and m are perpendicular, and rod l lies between them.

1. **Problem Statement:** Given a parallelogram REST with angles at vertices T, S, R, and E labeled as $x$, $y$, $45^\circ$, and $80^\circ$ respectively, find the values of $x$, $y

1. **Problem statement:** We need to find the length of edge $AD$ in a triangular pyramid with given angles and side $BC = 37$ cm. 2. **Given data:**

1. **Problem Statement:** Calculate the length of edge $AD$ in the given triangle-based pyramid, where angles at $D$, $A$, and $B$ are $39^\circ$, $44^\circ$, and $126^\circ$ respe

1. **Problem statement:** We have a circle with points P, Q, and R on its circumference. RT is a tangent at R and is parallel to chord PQ. Given PR = 8 cm and \(\angle QRT = 70^\ci

1. **Problem statement:** Given triangle ABC with sides AB = 18, BC = 24, and CA = 20. Point D is on AB such that AD = 15, and point E is on BC such that EC = 20. Lines AE and DC i

1. **Problem Statement:** Find the perimeter of trapezoid ABCD where AB is parallel to DC.

1. **Problem statement:** Given a circle with center $O$ and points $Q$, $R$, and $P$ on the circumference, where $OR = OP$ and $OQ = PQ$, and the central angle $\angle QOR = 70^\c

1. **State the problem:** We need to find the area of a circle with radius $r = 6$ miles. 2. **Formula:** The area $A$ of a circle is given by the formula:

1. **State the problem:** We need to find the area of a circle given its diameter is 14 kilometers. 2. **Formula:** The area $A$ of a circle is given by the formula $$A = \pi r^2$$

1. The problem states that the diameter $d$ of a circle is 8 centimeters, and we need to find the area of the circle rounded to the nearest hundredth. 2. Recall the formula for the

1. **Problem statement:** Find the perimeter of polygon ABCD where $m(\angle B) = m(\angle ACD) = 90^\circ$, $AB = 4$ cm, $BC = 3$ cm, and $AD = 13$ cm.

1. **State the problem:** Chu needs carpet for a square room with an area of 15 m². The carpet rolls are 3.8 m wide. We need to determine if the carpet can cover the room without s

1. **State the problem:** We have a square with an area of 225 cm², and we want to find the radius $r$ of the largest circle that can fit inside the square. 2. **Recall the formula

1. **Problem statement:** Given two parallel lines $\ell \parallel m$, and $\overrightarrow{DE}$ bisects $\angle CDF$, find the value of $y$. 2. **Understanding the problem:** Sinc

1. **Problem statement:** Given two parallel lines $l \parallel m$, and a ray $\overrightarrow{DE}$ that bisects $\angle CDF$, find the value of $y$. 2. **Understanding the problem

1. **Problem:** Find the length of segment NM in a circle with center K and radius 16. Points L and N lie on the circumference, M is outside the circle. Line segment MN intersects

1. **Problem:** Find the length of segment NM given that segments KL and MN are parts of chord KM in a circle, with lengths $x - 3$ and $x + 3$ respectively, and the entire chord K

1. **Problem statement:** We have an equilateral triangle QPR, and we are given that angle PRS equals $2x - 10^\circ$. We need to find the value of $x$. 2. **Important properties:*

1. The problem asks to identify an angle that is greater than 180° but less than 360°. 2. Angles are measured in degrees, and a full circle is 360°.

1. The problem asks to find an angle that is greater than 189° but less than 360°. 2. Angles are measured in degrees, and the range given is between 189° and 360°.