Tangent and Intersected Chord Theorem

Front

What is the Tangent and Intersected Chord Theorem?

Back

The Tangent and Intersected Chord Theorem states that if a tangent from a point outside a circle touches the circle at point A, and a chord BC is drawn through point A, then the angle formed between the tangent and the chord (∠CAB) is equal to the angle formed by the chord and the arc opposite to the angle (∠BDA).

Front

How do you find the measure of an angle formed by a tangent and a chord?

Back

To find the measure of the angle formed by a tangent and a chord, use the formula: ∠CAB = 1/2 (arc BD - arc AC).

Front

What is the relationship between the angles formed by intersecting chords?

Back

The angles formed by intersecting chords are related by the formula: ∠1 = 1/2 (arc AB + arc CD), where ∠1 is the angle formed by the intersection of chords AB and CD.

Front

If a tangent and a chord intersect at a point on the circle, what can be said about the angles?

Back

The angle formed between the tangent and the chord is equal to the angle formed by the chord and the arc opposite to it.

Front

What is the measure of an angle formed by two intersecting chords?

Back

The measure of an angle formed by two intersecting chords is equal to half the sum of the measures of the arcs intercepted by the angle.

Front

If the measure of arc AB is 80 degrees and arc CD is 100 degrees, what is the measure of the angle formed by the intersecting chords?

Back

The measure of the angle is (80 + 100) / 2 = 90 degrees.

Front

What is the formula to calculate the angle formed by a tangent and a chord?

Back

The formula is: ∠CAB = 1/2 (arc BD - arc AC).

Front

How do you calculate the measure of an angle formed by two intersecting chords?

Back

Use the formula: ∠1 = 1/2 (arc AB + arc CD).

Front

What is the significance of the Tangent and Intersected Chord Theorem in geometry?

Back

It helps in solving problems related to circles, particularly in finding unknown angles and lengths.

Front

If a tangent touches a circle at point A and a chord BC is drawn through A, what is the relationship between ∠CAB and arc BD?

Back

∠CAB = 1/2 (arc BD).