📐 geometry

1. The problem is to state the Circle Theorem. 2. The Circle Theorem states that the angle subtended by a diameter of a circle at any point on the circle is a right angle (90 degre

1. **Problem:** Calculate the unknown side of the triangle with sides 35 cm and 37 cm. 2. **Formula:** Use the Pythagorean theorem for right triangles: $$c^2 = a^2 + b^2$$ where $c

1. **State the problem:** We need to find the measure of the smallest angle in a triangle with sides 12, 23, and 34, where the smallest angle is opposite the side of length 12. 2.

1. **State the problem:** We need to find the measure of the largest angle in a triangle with sides 12, 23, and 34. The largest angle is opposite the longest side, which is 34. 2.

1. **State the problem:** Find the distance between the two parallel planes given by the equations: $$z=2y-2x$$

1. **State the problem:** We need to find the length of the arc AB of a sector of a circle with radius 43 mm and central angle 62°. 2. **Formula for arc length:** The length of an

1. **State the problem:** We need to find the surface area of a birdhouse with a rectangular base, a triangular prism roof, and a circular hole on the front triangular face.

1. **State the problem:** Determine the surface area of the birdhouse with a rectangular base of dimensions 26 cm by 25 cm, a height of 18 cm, and a triangular roof with slant heig

1. **Problem statement:** Given rays \(\overrightarrow{OC}\), \(\overrightarrow{OD}\), \(\overrightarrow{OE}\), \(\overrightarrow{OF}\), and \(\overrightarrow{OG}\) bisecting angle

1. **Problem statement:** Find the length of segment $DE$ given the geometric configuration with points $A, B, C, D, E, F, G$ and the following data: $AG=3$, $GB=7$, angles at $C$

1. **Problem 1: Area of parallelogram B** We are given two parallelograms A and B with bases 4 cm and 6 cm respectively.

1. **Problem:** Two similar triangles have bases 7 cm and 14 cm. Triangle A has area 20 cm². Find the area of triangle B. 2. **Formula:** Areas of similar triangles scale as the sq

1. **Problem 1: Areas of Similar Triangles** We have two similar triangles A and B.

1. **State the problem:** We need to find the length of the hypotenuse of a right triangle with legs 36 and 15. 2. **Recall the Pythagorean theorem:** For a right triangle with leg

1. **State the problem:** We need to find the length of the unknown leg of a right triangle where one leg is 12.75 and the hypotenuse is 37.25. 2. **Formula used:** In a right tria

1. **State the problem:** We need to find the area of a rectangle with length $2\sqrt{27}$ cm and width $4\sqrt{3}$ cm. 2. **Formula for area of a rectangle:**

1. **State the problem:** We need to find the measure of angle $m\angle XYW$ in the given triangle $XYZ$ with exterior point $W$ on segment $XY$. 2. **Given information:**

1. **Stating the problem:** We have two parallel horizontal lines intersected by two parallel diagonal lines, creating several angles. We want to find which angle facts can be used

1. The problem asks which angle fact can be used to find angle $h$ from angle $g$ when two parallel lines are cut by transversals. 2. Important angle facts when parallel lines are

1. **Stating the problem:** Find the volume of a cuboid given its total surface area is 300 cm², length $l=7$ cm, and breadth $b=16$ cm. 2. **Formula for surface area of a cuboid:*

1. **State the problem:** We need to find the measure of angle $\angle ABD$ in the quadrilateral $ABD$ where $\angle BAD = (7x + 1)^\circ$, $\angle ABD = (2x + 36)^\circ$, and side