Mix Examples - Circles Questions in English

(C) Since $AB$ is the diameter of the circle with centre $P$,the angle subtended by the diameter at any point on the circle is a right angle. Therefore,$\angle ACB = 90^\circ$.
In $\triangle ACB$,by the Pythagorean theorem,$AC^2 + BC^2 = AB^2$.
The radius of the circle is $34 \, cm$,so the diameter $AB = 2 \times 34 = 68 \, cm$.
Substituting the values,$32^2 + BC^2 = 68^2$.
$1024 + BC^2 = 4624$.
$BC^2 = 4624 - 1024 = 3600$.
$BC = \sqrt{3600} = 60 \, cm$.

(A) By definition,a line segment that connects the center of a circle to any point on its circumference is known as the radius of the circle. Therefore,the correct option is $A$.

(C) chord that passes through the centre of a circle is known as the diameter of the circle. The diameter is the longest chord of the circle and its length is twice the radius $(d = 2r)$.

(D) chord is a line segment whose endpoints lie on the circle. $A$ diameter is a special type of chord that passes through the centre of the circle. Since the distance between any two points on a circle is maximized when the line segment passes through the centre,the diameter is the longest chord of the circle.

(B) By definition,a circle is the collection of all points in a plane that are at a fixed distance from a fixed point. This fixed point is called the centre of the circle. Since every point on the circle lies at this fixed distance (the radius) from the centre,the centre is equidistant from every point on the circle.

(C) The perimeter or the total length of the boundary of a circle is known as its circumference. Therefore,the correct answer is circumference.

(A) circle that passes through all the vertices of a triangle is known as the circumcircle of that triangle. The center of this circle is called the circumcenter,and its radius is called the circumradius. Therefore,the correct term is circumcircle.

(B) sector of a circle is the portion of a disk enclosed by two radii and an arc,where the smaller area is known as the minor sector and the larger is the major sector. Therefore,the region defined is a sector.