📐 geometry

1. Stating Question 2: A compound curve has a common tangent length of 81.6 m, making angles $15^\circ$ and $17^\circ$ with the tangents of the first and second curves respectively

1. **State the problem:** We need to find the arc measure of the major arc \(\widehat{AEB}\) in a circle with diameters \(\overline{AD}\) and \(\overline{CE}\) intersecting at the

1. The problem states that \(\overline{AD}\) and \(\overline{CE}\) are diameters of circle \(P\). 2. Since \(AD\) and \(CE\) are diameters, \(A\), \(D\), \(C\), and \(E\) lie on th

1. **State the problem:** We need to find the arc measure of the major arc BÂD on circle P, given the central angles \(\angle APB = 136^\circ\), \(\angle BPC = 74^\circ\), and \(\a

A. Find the Measure of the Central Angle 1. Problem: Given the intercepted arc measures 72° in a circle, find the measure of the central angle.

1. The problem asks us to complete statements to prove triangle ABC is congruent to triangle ADC in rectangle ABCD with diagonal AC. 2. Since ABCD is a rectangle, angles ADC and AB

1. **State the problem:** We have an isosceles triangle ABC with vertices A(-9, 11), B(-9, 0), and C(p, q). AB is parallel to the y-axis, BC is parallel to the x-axis, and the area

1. **Problem Statement:** We have rectangle ABCD where AD = 34 cm. The rectangle is folded along line AP, bringing point B to side CD at point B'. We know \(\angle AB'D = 66^\circ\

1. **State the problem:** We have rectangle ABDE and parallelogram BCDF. We need to find the perpendicular distance from point B to line DF. 2. **Identify given measurements:**

1. Xác định biểu thức vector trong câu b): Biểu diễn vectơ \(\overline{AM} = (1-k) \overline{AB} + k \overline{AC} \)

1. Cho hình bình hành ABCD tâm O, M, N lần lượt là trung điểm AB, CD. - a) Ta có \(\overrightarrow{DA} + \overrightarrow{DB} = 2 \overrightarrow{DM}\) chứng minh sử dụng trung điểm

1. The problem states a triangle \(\triangle ABC\) with sides \(AB=5\), \(AC=6\), and \(\sin \angle BAC=0.1\). We need to find its area. 2. Recall the formula for the area of a tri

1. Problem 9 states: Circles P and Q are tangent at S. AB is tangent to both circles at S. Given AB = 16, AP = 12, AQ = 10, find length PQ if it bisects AB. 2. Since AB is tangent

1. **Stating the problem:** We have an equilateral triangle $ABC$ and points $M, N, P$ defined by $BM = kBC$, $CN = \frac{2}{3}CA$, and $AP = \frac{4}{15}AB$. We examine the claim

1. **State the problem:** We are given two ellipses (Figure 1 and Figure 2) centered at the origin (0,0). 2. **Figure 1 details:**

1. Problem: Analyze the ellipses in Figures 1 and 2 and find the center, vertices, co-vertices, foci, lengths of axes, and equations for each. **Figure 1:**

1. **Stating the problem:** We have three power stations K, L, and M with the following information:

1. Show that [MR] and [AS] are the perpendicular bisectors of each other in square MARS. Since MARS is a square, all sides are equal and angles are $90^\circ$.

1. Stating the problem: Find the distance from the point $(2,3)$ to the straight line given by the equation $$4x + 3y = 10$$. 2. Formula for the distance $d$ from a point $(x_0, y_

1. Stating the problem: Find the cross-sectional area, lateral surface area, total surface area, and volume for each prism (a) through (च). 2. Prism (a): Rectangular prism with len

1. **Rectangular prism (a): length = 10 cm, width = 6 cm, height = 8 cm** - Cross-sectional area (base area): $A = \text{length} \times \text{width} = 10 \times 6 = 60 \text{ cm}^2