Question

The intersecting chords theorem states we can calculate the angle measure by... *

A. Adding the values of the intercepted arcs and that is equal to twice the angle measure.

B. Subtracting the values of the intercepted arcs and that is equal to twice the angle measure

C. The angles and the arcs are the same measure

D. The angle is half the measure of the arc

Answer 1

A. Adding the values of the intercepted arcs and that is equal to twice the angle measure

Explanation:

The intersecting chords theorem states that when four line segments are formed by two chords intersecting in a circle, the product of the two line segments on one chord is equal to the product of the two line segments on the other chord

The angles of intersecting chords theorem states that the angles formed by the intersecting chords one half the sum of the arcs intercepted by the chords

In the diagram attached, we have;

∠x = ∠y + ∠z

m
`\widehat{DHE}` = 2·∠z, m
`\widehat{CIF}` = 2·∠y

∴ ∠x = (1/2) × m
`\widehat{DHE}` + m
`\widehat{CIF}`

m
`\widehat{DHE}` + m
`\widehat{CIF}` = 2 × ∠x

The correct option is therefore adding the values of the intercepted arcs and that is equal to twice the angle measure.