Question

Segment AC is a tangent of Circle O and Circle P
Segment AC = 24
Segment OC = 26
Segment OP = 13
Segment BP = ___
Hint: Use the Pythagorean Theorem and then Proportions to find the value

Answer 1

13^2+24^2=26^2?

Answer 2

OAC is a right triangle.
Find OA first.
OA^2 + AC^2 = OC^2

Answer 3

I came up with OA=10

Answer 4

correct. Next find PC. PC = OC - OP = ?

Answer 5

PC=13

Answer 6

correct. Triangles BPC and AOC are similar.
Therefore, BP / AO = PC / OC
BP = PC / OC * AO = ?

Answer 7

PC = 13 (see your previous calculation)
OA = 10 (see your calculation before that)
OC = 26 (given)

BP = PC / OC * AO = 13 / 26 * 10 = 10/2 = 5

Answer 8

Thank you