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An isosceles right triangle is inscribed in a circle Find the radius of the circle if one leg of the triangle is 8 cm?
Wiki User
∙ 11y ago
First you half all the sides, so 4cm, them you multiply by pi, giving the radius as 12pi, or 12.56637061
Wiki User
∙ 11y ago
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Prove that the tangent at a to the circumcircle of triangle abc is parallel to bc where triangle abc is a isosceles triangle?
The circumcircle of a triangle is the circle that passes through the three vertices. Its center is at the circumcenter, which is the point O, at which the perpendicular bisectors of the sides of the triangle are concurrent. Since our triangle ABC is an isosceles triangle, the perpendicular line to the base BC of the triangle passes through the vertex A, so that OA (the part of the bisector perpendicular line to BC) is a radius of the circle O. Since the tangent line at A is perpendicular to the radius OA, and the extension of OA is perpendicular to BC, then the given tangent line must be parallel to BC (because two or more lines are parallel if they are perpendicular to the same line).
How do you find the ratio of a circle inscribed a rhombus?
A rhombus is a flexible shape which can range from almost a square to a very narrow shape. A rhombus with sides of x cm can contain a circle with any radius less than x/2 cm. The information in the question is insufficient to determine the radius. And a ratio requires some characteristic of the inscribed circle to be compared to an analogous characteristic of another shape.
What is the area of a circle inscribed in a square of area 2 metersquare?
A square with an area of 2 m2 has sides of sqrt(2) m. The diameter of the inscribed circle is, therefore sqrt(2) m. The radius is sqrt(2)/2 m The area of a circle with radius sqrt(2)/2 is pi*[sqrt(2)/2]2 = pi*2/4 or pi/2 = 1.5708 m2
The perimeter of the square is 16 inches what is the circumference?
The perimeter of a plane figure is the length of its boundary. Thus the perimeter of a square of length L is 4L. So the perimeter of a square of length 4 is 4 x 4 = 16 (4 + 4 + 4 + 4 = 16). The perimeter of a circle is the length of its circumference.If you are asking for the circumference of the circle circumscribed and inscribed in this square, their circumference will be:First, we need to find the measure length of their radius. We know that the diagonals of the square form 4 congruent isosceles triangles with the base length equal to the length of the square, and length side equal one half of the diagonal length ( the diagonals of a square are equal in length and bisect each other (and bisect also the angle of the square ), so the center of the circumscribed circle of the square will be the point of their intersection, and its radius will be the one half of the diagonal of the square). We can find the diagonal length by using the Pythagorean theorem. So from the right trianglewhich is formed by drawing one of the diagonals, we find the length of the diagonal which is also the hypotenuse of this right triangle, and which is equal to square root of[2(4^2)]. So the length of the diagonal is equal 4(square root of 2), and its half is 2(square root of 2), which is the length of the radius of the circumscribed circle. So its circumference is equal to (2)(pi)(2(square root of 2)) = 4(square root of 2)pi.Now, we need to know what is the length of the radius of the inscribed circle, and what is this radius. Let's look at the one of the fourth triangles that are formed by drawing the two diagonals of the square. If we draw the perpendicular from the intersection of the diagonals to the side of the square, this perpendicular is the median of the side of the square and also the altitude of this isosceles triangle. Let's find the measure of its length. Again we can use the Pythagorean theorem. So this measure is equal to the square root of [(2(square root of 2))^2] - 2^2] which is equal to 2. If we extend this perpendicular to the side of the triangle and draw another perpendicular from the point of the intersection of the diagonals to the other sides of the square, their length will be also 2. Since they have the same distance from the point of the intersection of the diagonals, we can say that their length is the length of the radius of the inscribed circle, and the point of the intersection of the diagonals is also its center. So the measure of length of the radius is 2, and the circumference of the inscribed circle is (2)(pi)(r) = (2)(pi)(2) = 4pi.As a result, we can say that the point of the intersection of the diagonals of a square is the center of its inscribed and circumscribed circle, and the perpendicular lines drawing from this point to the sides of the square bisect each other. (These perpendiculars are parallel and equal in length to the square length, because we know that two lines that are perpendicular respectively to the other two parallel lines, are equal in length and parallel between them). We also can say that in an isosceles triangle with 45 degrees base angle, the median is not only also an altitude, but its length is one half of the length of the base.
A square is inscribed in a circle of radius 7cmFind the area of square and the area shaded?
The area of the square is 98 square cm. Assuming the shaded area is the remainder of the circle, its area is 55.9 square cm (approx).
The shortest distance from the center of the inscribed circle to the triangle's sides is the circle's?
radius
Is an isosceles trapezoid always inscribed in a circle?
If you want to, you can always draw a circle around an isosceles trapezoid and the radius can be half the base of the trapezoid.
Does a triangle have a radius?
It has at least two radii, the radius of the circle going through the vertices and the radius of the inscribed circle touching all the sides.
The shortest distance from the center of the circumscribed circle to the vertices of the inscribed triangle is the circle's radius?
True
What is the formula for equillateral triangle?
There are different formula for: Height, Area, Perimeter, Angle, Length of Median Radius of inscribed circle Perimeter of inscribed circle Area of inscribed circle etc.
Is the shortest distance from the center of the circumscribed circle to the vertices of the inscribed triangle is the circles radius?
True
The shortest distance from the center of the circumscribed circle to the sides of the inscribed triangle is the circles radius?
FALSE
Is the distance from the point of concurrency of the angle bisectors of a triangle to a point on the inscribed circle is the radius of the circle True or False?
false
Is the distance from the point of concurrency of the angle bisectors of a triangle to a point on the inscribed circle is the radius of the cirlce?
yes
How would you construct an isosceles triangle if only given the vertex angle and the radius of the circumscribed circle?
You have an isosceles triangle, and a circle that is drawn around it. You know the vertex angle of the isosceles triangle, and you know the radius of the circle. If you use a compass and draw the circle according to its radius, you can begin your construction. First, draw a bisecting cord vertically down the middle. This bisects the circle, and it will also bisect your isosceles triangle. At the top of this cord will be the vertex of your isosceles triangle. Now is the time to work with the angle of the vertex. Take the given angle and divide it in two. Then take that resulting angle and, using your protractor, mark the angle from the point at the top of the cord you drew. Then draw in a line segment from the "vertex point" and extend it until it intersects the circle. This new cord represents one side of the isosceles triangle you wished to construct. Repeat the process on the other side of the vertical line you bisected the circle with. Lastly, draw in a line segment between the points where the two sides of your triangle intersect the circle, and that will be the base of your isosceles triangle.
The radius of a incircle is 14cm what is the side of the equilateral triangle abc?
Where the side of the equilateral triangle is s and the radius of the inscribed circle is r:s = 2r * tan 30° = 48.50 cm
Is the shortest distance from the center of the inscribed circle to the triangle sides is the circles?
It is its inradius.
