![]() ![]() #-># But if this means that and the isosceles triangle of maximum area is also an equilateral triangle. This is the largest equilateral that will fit in the circle, with each vertex touching the circle. #d/(dalpha)(S_(triangle_(ABC)))=4r^2 cos(alpha/2)*(1/2)cos^3(alpha/2)+4r^2 sin(alpha/2)*3cos^2(alpha/2)(-sin(alpha/2))(1/2)# How to construct (draw) an equilateral triangle inscribed in a given circle with a compass and straightedge or ruler. Since in this problem #r# is constant, we need to find the derivative relatively to #alpha# of #S_(triangle_(ABC))# and equal it to zero to find the maximum or minimum of the area of the triangle. ![]() Then we can obtain the area of the triangle in function of #r# and #alpha#: Replacing #a# for its value in function of #r# and #alpha#: The base angle is equal to quantity 180° minus vertex angle, divided by 2. Use the following formula to solve either of the base angles: 180° / 2. Given any angle in an isosceles triangle, it is possible to solve the other angles. #tan(alpha/2)=(a/2)/h# => #h=a/(2tan(alpha/2))# How to Calculate the Angles of an Isosceles Triangle. We can obtain the height #h# in function of #r# and #alpha# in this way: Since => #a=rsin alpha *cancel(cos alpha))/cancel(cos alpha)# Suppose the top vertex is A A, the right vertex is B B and the left vertex is C C. (c) Identify the type of triangle of maximum area. ABC A B C is an isosceles triangle inscribed in a circle with centre O O. 294 41K views 6 years ago Write Standard Quadratic Equation from Radical Roots Alternate Solution with Trig: Thanks Mondal to ask how the property of. (b) Solve by writing the area as a function of a. the circle into two sectors, called correspondingly the major sector OAB and. ![]() (a) Solve by writing the area as a function of h. BO form an isosceles triangle whose base is the chord. We can obtain the side #a# in function of #r# and #alpha# in this way (Law of Sines applied to #triangle_(BCD)#): Transcribed Image Text: Find the area of the largest isosceles triangle that can be inscribed in a circle of radius r 14 (see figure). Suppose an isosceles #triangle_(ABC)# inscribed in a circle with center in #D# and radius #r#, like the figure below. However if you need a formal demonstration of this statement read the first part of this explanation. One could start by saying that the isosceles triangle with largest area inscribed in a triangle is also an equilateral triangle. ![]()
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