Which fits better a round peg in a square hole or a square peg in a round hole?

Which fits better a round peg in a square hole or a square peg in a round hole?

The circle covers more of the square than the square does the circle. It’s therefore better to be a round peg in a square hole than a square peg in a round hole. Alternatively they may then subtract the area of the circle from the square area to find the wasted area.

What is the area of the largest circle?

• Therefore diameter of circle =14 cm.
• Hence area of circle=πr2.
• =154cm2.

What is the area of the largest circle that can be drawn inside a square of side 20cm?

so, the area of the circle is 22/7 x 14 cm2 = 44 cm.

Is the area of the circle inscribed in a square of side a CM?

Answer. Answer: Step-by-step explanation: The side of the square = a cm.

What is the radius of the incircle of a triangle?

Its radius, the inradius (usually denoted by r) is given by r = K/s, where K is the area of the triangle and s is the semiperimeter (a+b+c)/2 (a, b and c being the sides).

What is the radius of the circle circumscribing an isosceles triangle?

Problem Answer: The radius of the circle circumscribing an isosceles right triangle is 12.73 m.

How do you find the radius of a Circumcircle?

Derivation of Formula for Radius of Circumcircle

1. From triangle BDO. sinθ=a/2R.
2. sinθ=a2R.
3. At=abc4R.

Where is the Circumcenter of an isosceles triangle?

The circumcenter of an obtuse isosceles triangle is outside the triangle and the perpendicular bisector passes through the obtuse angle of the triangle. Let’s also note where the circumcenter gets its name. The circumcenter is also the center of circle that the triangle is circumscribed inside of.

How do you find the Circumcenter of an isosceles triangle?

To find the circumcenter of any triangle, draw the perpendicular bisectors of the sides and extend them. The point at which the perpendicular intersects each other will be the circumcenter of that triangle.

What is the equidistant from the sides of a triangle?

The incenter is equidistant from the sides of the triangle. That is, PI=QI=RI . The circle drawn with the incenter as the center and the radius equal to this distance touches all three sides and is called incircle or the inscribed circle of the triangle.

Is the Orthocenter always inside the triangle?

The orthocenter is always outside the triangle opposite the longest leg, on the same side as the largest angle. The only time all three of these centers fall in the same spot is in the case of an equilateral triangle.

Why is the Incenter equidistant from the sides of a triangle?

The angle bisectors of the angles of a triangle are concurrent (they intersect in one common point). The point of concurrency of the angle bisectors is called the incenter of the triangle. Since radii in a circle are of equal length, the incenter is equidistant from the sides of the triangle.

What is Orthocentre of a triangle?

The orthocenter is the point where all three altitudes of the triangle intersect. An altitude is a line which passes through a vertex of the triangle and is perpendicular to the opposite side. There are therefore three altitudes in a triangle.

Is the Orthocenter equidistant from the sides?

The ORTHOCENTER of a triangle is the common intersection of the three lines containing the altitudes. Since a point interior to an angle that is equidistant from the two sides of the angle lies on the angle bisector, then the Incenter must be on the angle bisector of each angle of the triangle.

Is the Incenter equidistant from the sides?

The incenter may be equivalently defined as the point where the internal angle bisectors of the triangle cross, as the point equidistant from the triangle’s sides, as the junction point of the medial axis and innermost point of the grassfire transform of the triangle, and as the center point of the inscribed circle of …

What is the Circumcenter Theorem?

Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. Since OA=OB=OC , point O is equidistant from A , B and C . This means that there is a circle having its center at the circumcenter and passing through all three vertices of the triangle.

Which points of concurrency are always inside the triangle?

• The centroid is the point of concurrency of the three medians in a triangle.
• It is the center of mass (center of gravity) and therefore is always located within the triangle.

What is it called when three or more lines intersect at the same point?

A set of lines or curves are said to be concurrent if they all intersect. at the same point. In the figure below, the three lines are concurrent because they all intersect at a single point P. The point P is called the “point of concurrency”.

Can 3 lines intersect at one point?

Three intersecting lines can share a common point of intersection. Two intersecting lines form two pairs of vertical angles. Two intersecting lines form four pairs of vertical angles. Three intersecting lines can never share four common points of intersection.

What is the point of concurrency for altitudes?

The orthocenter is the point of concurrency of the three altitudes of a triangle. To understand what this means, we must first determine what an altitude is. An altitude is a line that passes through a vertex of a triangle and that is perpendicular to the line that contains the opposite side of said vertex.

What is the intersection of the three altitudes in a triangle?

orthocenter