Inscribed Circles

Front

What is an inscribed circle?

Back

An inscribed circle is a circle that is drawn inside a polygon such that it touches all the sides of the polygon at exactly one point each.

Front

What is the relationship between the angles and arcs in a circle?

Back

The measure of an inscribed angle is half the measure of the intercepted arc.

Front

How do you find the measure of an angle formed by two chords that intersect inside a circle?

Back

The measure of the angle is equal to half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

Front

What is the formula for the area of a circle?

Back

The area of a circle is given by the formula A = πr², where r is the radius of the circle.

Front

What is the relationship between the radius of an inscribed circle and the sides of the polygon?

Back

The radius of an inscribed circle (inradius) is the distance from the center of the circle to any side of the polygon.

Front

How do you calculate the measure of an arc in a circle?

Back

The measure of an arc can be calculated using the formula: Arc Measure = (Central Angle / 360) * Circumference of the Circle.

Front

What is the significance of the central angle in relation to the inscribed angle?

Back

The inscribed angle is always half the measure of the central angle that subtends the same arc.

Front

What is the relationship between the angles formed by tangents and chords?

Back

The angle formed by a tangent and a chord through the point of contact is equal to the measure of the opposite arc.

Front

How do you find the measure of an exterior angle formed by two secants?

Back

The measure of the exterior angle is equal to half the difference of the measures of the intercepted arcs.

Front

What is the formula for the circumference of a circle?

Back

The circumference of a circle is given by the formula C = 2πr, where r is the radius.