Question

If the blue radius below is perpendicular to the chord AC which is. 14 units long, what is the length of the segment AB?

Answer 1

7 units

Explanation:

Answer 2

C. 7 units

Explanation:

The given parameters are;

The length of the chord of the circle,
`\overline{AC}` = 14 units

The orientation of the radius and the chord = The radius is perpendicular to the chord

We have in ΔAOC,
`\overline{AO}` =
`\overline{OC}` = The radius of the circle

`\overline{OB}` ≅
`\overline{OB}` by reflexive property

The angle at point B = 90° by angle formed by the radius which is perpendiclar to the chord
`\overline{AC}`

ΔAOB and ΔCOB are right triangles (triangles having one 90° angle)

`\overline{AO}` and
`\overline{OC}` are hypotenuse sides of ΔAOB and ΔCOB respectively and
`\overline{OB}` is a leg to ΔAOB and ΔCOB

Therefore;

ΔAOB ≅ ΔCOB, by Hypotenuse Leg rule of congruency

Therefore;

`\overline{AB}` ≅
`\overline{BC}` by Congruent Parts of Congruent Triangles are Congruent, CPCTC

`\overline{AB}` =
`\overline{BC}` by definition of congruency

`\overline{AC}` =
`\overline{AB}` +
`\overline{BC}` by segment addition postulate

∴
`\overline{AC}` =
`\overline{AB}` +
`\overline{BC}` =
`\overline{AB}` +
`\overline{AB}` = 2 ×
`\overline{AB}`

∴
`\overline{AB}` =
`\overline{AC}`/2

`\overline{AB}` = 14/2 = 7

`\overline{AB}` = 7 units.