📐 geometry

1. Bài toán: Cho ΔABC có ba góc nhọn, O là giao điểm hai đường trung trực của AB và AC. Trên tia đối của tia OB lấy điểm D sao cho OB = OD. 2. Chứng minh O thuộc đường trung trực c

1. The problem asks which circle has its circumference labeled in red. 2. The circumference of a circle is the total distance around the circle, i.e., the outer edge.

1. **State the problem:** Find the area of a triangle with base $10$ cm and height $8$ cm. 2. **Formula:** The area $A$ of a triangle is given by the formula:

1. The problem asks whether Cavalieri's principle states that two solids with equal heights and cross-sectional areas at every level have equal volumes. 2. Cavalieri's principle is

1. **State the problem:** Find the volume of the given triangular prism with dimensions: height of the triangle base $=5$, base edges $7$ and $8$. 2. **Formula for volume of a pris

1. **State the problem:** Find the lateral surface area of a square pyramid with base edge length 6 ft and slant height 11 ft. 2. **Formula:** The lateral surface area (LSA) of a s

1. **State the problem:** We have two triangles sharing a common base with congruent sides on the left. The upper triangle has an angle of 68° and side length 77 on the right, whil

1. The problem is to draw a circle and explain how to find the length of an arc of the circle. 2. A circle is a set of points equidistant from a center point. The length of an arc

1. **Problem statement:** Calculate the surface area of a triangular prism with base side length $a=6$ cm, height of the triangle $h_a=5.2$ cm, and prism height $h_k=19.8$ cm. 2. *

1. **State the problem:** We have a circle with center O and points A, D, B, E on the circle. Lines AFBC, OEC, and OFD are straight lines with given lengths: AF = 7 cm, FB = 4 cm,

1. **Problem Statement:** We have a map with points Q, P, A, and B arranged in a rectangular grid with given distances. We need to draw an accurate map using a suitable scale and d

1. **State the problem:** We have a circle centered at point $Q$ with a vertical diameter line passing through points $A$, $Q$, and $B$. The top and bottom horizontal chords are ea

1. **Problem statement:** We have a straight line WXYZ passing through the centers of two circles. Given the ratios: - $WX : XY = 7 : 2$

1. **State the problem:** We are given a circle tangent to a vertical line and a slanted line, with angles labeled 17x° and 75°. We need to solve for $x$. 2. **Identify the relatio

1. **State the problem:** Joe wants to find the total area of the front of his house that he needs to paint. This area is the total front area minus the areas of the door and windo

1. The problem asks to find the area of the shaded region in a trapezoid where the base of the triangle is the median of the trapezoid. 2. Recall the formula for the area of a trap

1. The problem asks to calculate the area of a circle with radius $r=3$ inches. 2. The formula for the area of a circle is $$A = \pi r^2$$ where $\pi \approx 3.14$.

1. **State the problem:** Calculate the area of a circle with radius 11 inches. 2. **Formula:** The area $A$ of a circle is given by the formula:

1. **Problem Statement:** Calculate the size of angle $EDC$ given the angles at points $B$, $C$, $E$, and $A$ in the geometric figure. 2. **Given Angles:**

1. **Stating the problem:** We need to calculate the size of angle $EDC$ given the other angles in the figure. 2. **Understanding the problem:** The points and angles given are $B=

1. **Problem statement:** You want a triangle drawn, and you want to know how to find its angles. 2. **Important rule:** The angles in any triangle always add up to $$180^\circ$$.