Question
Which theorem is used to derive the standard equation of a circle?
- Pythagoras theorem
- Thales’s theorem
- Euclid theorem
- None of these
Hint:
We get a right triangle with x ,y as sides and r as Hypotenuse of the right triangle formed in the circle.
Therefore, The possible Theorem is Pythagorean Theorem.
The correct answer is: Pythagoras theorem
Let (x, y) represent any point on a circle with center at the origin and radius r.
Here, x and y are the side lengths of the right triangle and r is the Hypotenuse of right triangle
By the Pythagorean Theorem,
This is the equation of a circle with radius and center at the origin.
Related Questions to study
If two chords are congruent then their respective arcs are_____________.
Two figures are said to be congruent if they are identical to each other or they superimpose on each other completely. In a circle two chords will be congruent only if their lengths are equal.
If two chords are congruent then their respective arcs are_____________.
Two figures are said to be congruent if they are identical to each other or they superimpose on each other completely. In a circle two chords will be congruent only if their lengths are equal.
The measure of an inscribed angle is _____________ the measure of its intercepted arc
Intercepted arc is a part of the circle’s circumference which is formed when two lines passes through the circle and meet at a point inside the circle. The angle formed at the point of intersection is called inscribed angle.
The measure of an inscribed angle is _____________ the measure of its intercepted arc
Intercepted arc is a part of the circle’s circumference which is formed when two lines passes through the circle and meet at a point inside the circle. The angle formed at the point of intersection is called inscribed angle.
If two inscribed angles of a circle intercept ____________ Arc, the angles are congruent
If two inscribed angles of a circle intercept ____________ Arc, the angles are congruent
The line which intersects the circle at one point is called_____________
The line which intersects the circle at one point is called_____________
If a tangent and secant, two tangents or two secants intersect outside a circle, then the measure of the angle is one half the _____________ of the measures of the intercepted arcs.
Intercepted arc is a part of the circle’s circumference which is formed when two lines passes through the circle and meet at a point inside the circle. The angle formed at the point of intersection is called inscribed angle.
If a tangent and secant, two tangents or two secants intersect outside a circle, then the measure of the angle is one half the _____________ of the measures of the intercepted arcs.
Intercepted arc is a part of the circle’s circumference which is formed when two lines passes through the circle and meet at a point inside the circle. The angle formed at the point of intersection is called inscribed angle.
Inscribed angle is half the measure of its _____________.
Intercepted arc is a part of the circle’s circumference which is formed when two lines passes through the circle and meet at a point inside the circle. The angle formed at the point of intersection is called inscribed angle.
Inscribed angle is half the measure of its _____________.
Intercepted arc is a part of the circle’s circumference which is formed when two lines passes through the circle and meet at a point inside the circle. The angle formed at the point of intersection is called inscribed angle.
If two chords intersect inside a circle, then the measure of each angle is one half the _____________ of the measures of the arcs intercepted by the angle and its vertical angle.
Vertical angles are a pair of opposite angles which are formed when two lines intersect with each other.
Intercepted arc is a part of the circle’s circumference which is formed when two lines passes through the circle and meet at a point inside the circle. The angle formed at the point of intersection is called inscribed angle.
If two chords intersect inside a circle, then the measure of each angle is one half the _____________ of the measures of the arcs intercepted by the angle and its vertical angle.
Vertical angles are a pair of opposite angles which are formed when two lines intersect with each other.
Intercepted arc is a part of the circle’s circumference which is formed when two lines passes through the circle and meet at a point inside the circle. The angle formed at the point of intersection is called inscribed angle.
