Points B and D are points of tangency. Find the value of x.12210204021.jpg

Two circles, whose radii are 12 inches and 16 inches respectively, intersect. The angle between the tangents at either of the points of intersection is ${\displaystyle {20}^{\circ },{30}^{\prime }}$. Find the distance between the centers of the circle.

Three pipes, each of radius length 4 in., are stacked as shown. What is the exact height of the stack?

If the atomic radius of lead is 0.175 nm, calculate the volume of its unit cell in cubic meters

Five circles are placed in a rectangle as shown. If the length of the shorter side of the rectangle is 1, find the length of the other side.

James has two circles, Circle A and Circle B. Use the information to answer the questions that follow.
Circle A: The equation for circle A is ${\displaystyle x^2+y^2+6x-4y-12=0}$
Circle B: center ${\displaystyle (0,-4)}$ with a radius of 3
A) Complete the square in order to find the center and radius of Circle A. Show your work and state the center and radius of the circle.
B) Does the point ${\displaystyle (\sqrt{8},-3)}$ lie on Circle B? Support your answer with evidence graphically or algebraically.
C) Are Circle A and Circle B similar? Yes or no and prove your answer.

Construct the complement of the acute angle Q shown.

Construct two circles with radius 1cm and 2cm respectively and centers 4cm apart , make two arcs with 5cm radius , internally tangential to both circles. Make sure you allow enough space for your work.