📐 geometry

1. **Problem:** Draw a line AB 60 mm long and bisect it. **Step 1:** Draw a straight line segment AB of length 60 mm.

1. **Problem:** Draw a line segment AB 60 mm long and bisect it. 2. **Formula and rules:** To bisect a line segment means to divide it into two equal parts at its midpoint.

1. **Stating the problem:** We are given the curved surface area formula of a cone: $$A = \pi r \sqrt{h^2 + r^2}$$

1. **State the problem:** We have a right-angled triangle with hypotenuse length $b$ cm and other sides $f$ cm and $g$ cm.

1. **Problem:** Which theorem or postulate can be used to show $\triangle GBE \cong \triangle ABD$? 2. **Recall the common triangle congruence postulates:**

1. **Problem statement:** We have a board of length 14.5 cm leaning against a vertical wall 10.5 cm high. The angle between the ground and the board is $a$ (in degrees). We want to

1. **Problem statement:** Find the value of $k$ and the area of a trapezium given certain conditions (not specified in the question, so we assume $k$ is a parameter related to the

1. **State the problem:** We have a trapezium PQRS with parallel sides PQ and SR. PQ = $2k + 2$ cm, SR = $4k - 1$ cm, height QR = $3k$ cm, and area $L = 150$ cm². We need to expres

1. **Problem statement:** Given trapezium AECB with AE \parallel BC, find the angles $\angle x$, $\angle y$, and $\angle z$. 2. **Key property:** In trapezium AECB, since AE is par

1. **State the problem:** We have two similar quadrilaterals CDEF and SRUT. Given the side lengths of CDEF: $CD=30$, $DE=63$, $EF=39$, $FC=81$, and some sides of SRUT: $TU=13$, $UR

1. **Problem statement:** We have an analogue clock with an hour hand of length 5 cm and a minute hand of length 10 cm. At 6:00, after $x$ minutes ($0 < x < 60$), the hour and minu

1. **Stating the problem:** We are given a circle with points S, T, U, P, Q, R on its circumference and a point O inside the circle. We know the angle at T formed by points S, T, U

1. Problem: Two right triangles $\triangle PQR$ and $\triangle ABC$ are given. 2. In $\triangle PQR$ the right angle is at $Q$, so $\angle Q=90^\circ$.

1. **Problem statement:** In triangle ABC, AB = AC, and the angle bisector of \(\angle ABC\) intersects AC at D. Given that \(BC = BD = AD\), find the measure of \(\angle CBD\). 2.

1. a. Find $w$ given arcs 110° and 70° in a circle with inscribed angle $w$. - The inscribed angle theorem states: an inscribed angle equals half the measure of its intercepted arc

1. **Stating the problem:** Find the area of the shaded rectangular face of the 3D prism with dimensions 9 m, 5 m, and 7 m.

1. **Problem Statement:** Find the length of the segment $x$ in a circle where a chord of length 10.2 is given, a perpendicular segment from the chord to the circle center is 8, an

1. The problem is to find the total number of triangles in a large square subdivided into a 5x5 grid with diagonal lines from each corner and additional diagonals in the central 3x

1. **Problem Statement:** Given a triangle $\triangle ABC$ with $AB = BC$ and $\angle ABC = 60^\circ$, find the area of $\triangle ABC$. 2. **Known Information:**

1. Problem statement. A cuboid has length $12$, width $9$, and height $4$.

1. **Problem Statement:** Find the standard form of the equation of a circle given different conditions. 2. **Formula:** The standard form of the equation of a circle with center a