Question

In circle p, td¯¯¯¯¯ and tb¯¯¯¯¯ intersect at t. ta=10, tc=8, cd=12, and ab=x+2. find ab. circle p. answer

Answer 1

The answer is AB = 6.

External value x (external value + internal value) = 
External value x (external value + internal value) of the other side

Substitute, transpose, and simplify.

TA x (TA + AB) = TC x (TC + CD)
10 x (10 + (x + 2)) = 8 x (8 + 12)
120 + 10x = 160
10x = 40
x = 4

To find AB: x + 12; x = 4
AB = x + 2
AB = 4 + 2
AB = 6