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

C. 7 units

Step-by-step explanation:

The given parameters are;

The length of the chord of the circle, = 14 units

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

We have in ΔAOC, = = The radius of the circle

≅  by reflexive property

The angle at point B = 90° by angle formed by the radius which is perpendiclar to the chord

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

and are hypotenuse sides of ΔAOB and ΔCOB respectively and is a leg to ΔAOB and ΔCOB

Therefore;

ΔAOB ≅ ΔCOB, by Hypotenuse Leg rule of congruency

Therefore;

≅ by Congruent Parts of Congruent Triangles are Congruent, CPCTC

= by definition of congruency

= + by segment addition postulate

∴ = + =   + = 2 ×  

∴   = /2

= 14/2 = 7

= 7 units.

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