📐 geometry

1. **Problem statement:** We have a circle with points F, G, H, and D on it. F and H lie on a horizontal diameter, with F on the left and H on the right. G is at the top of the cir

1. **State the problem:** Given triangle $\triangle ABC$ with points $A(0,0)$, $B(0,a)$, and $C(a,0)$, prove that median $AD$ is also an altitude. 2. **Identify point $D$:** Since

1. The problem asks to identify which segment among OK, VU, OS, and SH is a chord. 2. A chord is a segment with both endpoints on the circumference of the same circle.

1. The problem asks to identify the highlighted part of circle O. 2. The highlighted part is a line segment from the center O to a point V on the circle.

1. **State the problem:** We are given a rectangular prism with surface area 290 in², and dimensions including edges 11 in, 3 in, and an unknown edge $x$. We need to find $x$. 2. *

1. **Problem statement:** We have a kite-shaped quadrilateral with angles 50° at the top-left vertex and 80° at the lower-left interior angle near the diagonal intersection. We nee

1. **State the problem:** We have a kite-shaped polygon with angles 50°, 80°, and two unknown angles $x$ and $y$. We need to find the values of $x$ and $y$. 2. **Recall kite proper

1. **State the problem:** Solve for the unknown variable $x$ in each proportion given by the figures. 2. **Recall the proportion rule:** If two ratios are equal, then their cross p

1. **State the problem:** We need to find the area of a regular hexagon given its apothem length $10\sqrt{3}$ cm and the total area $1038$ cm². 2. **Formula for the area of a regul

1. **State the problem:** We need to find the missing edge length $w$ of a rectangular prism given its volume $V = 1.824$ m$^3$, and two known edges $3.8$ m and $0.6$ m. 2. **Formu

1. **State the problem:** Find the circumference of a circle given the diameter is 12 inches. 2. **Formula:** The circumference $C$ of a circle is given by the formula:

1. **Stating the problem:** Determine the lengths into which a leg (cateto) of length $a$ in a right triangle is divided by a chord perpendicular to that leg, such that the chord d

1. **State the problem:** We need to find the amount of paper needed to cover the side of a cylindrical can. The can has a diameter of 10 cm and a height of 8 cm.

1. **State the problem:** Find the surface area of a cylinder with base radius $r=2$ m and height $h=4$ m. 2. **Formula for surface area of a cylinder:**

1. **State the problem:** We need to find the perimeter of the given irregular polygon with sides labeled 30 mm, 15 mm, 20 mm, and 40 mm, plus the slanting right side. 2. **Identif

1. **State the problem:** Find the area of a trapezoid with top base $7$, bottom base $15$, and height $8$. 2. **Formula for the area of a trapezoid:**

1. **State the problem:** Find the area of the shaded kite-shaped region with vertical diagonal length 8 and horizontal diagonal length 8 (since two half-segments of 4 each sum to

1. **State the problem:** We have two secants, HIJ and LKJ, intersecting outside the circle at point J. Given lengths are $JI=31$, $JK=32$, and $KL=16$. We need to find the length

1. **Problem 5: Find the measures of angles 1, 2, 3, and 4 in the triangle figure.** 2. The triangle has angles 59°, 22°, and the angles labeled 1, 2, 3 inside it, plus an exterior

1. **State the problem:** Given circle A with points A, B, and C on the circumference, and interior point D such that \(m\angle ADB = 86^\circ\), find \(m\angle ACB\).

1. **Find the measure of arc ZWX (mZWX).** Given: Angle near chord is 115°.