Question

Circle problem #2

Answer 1

in that case,

AT^2 = (AC)(AB)

Answer 2

so AT = 15cm

Answer 3

@cuty_shai2000 Would you mind explaining what AT^2 = (AC)(AB) ?

Answer 4

by Cross-Product Property

Answer 5

Sorry... Do you mind explaining it in details?

Answer 6

I don't get what you mean.

Answer 7

ok wait

Answer 8

you mean the proof of the property?

Answer 9

Hmm.. at least what it is and how it can be applied here.

Answer 10

ah ok

Answer 11

i think she is right.

Answer 12

she is right, the only problem is that i don't understand, sorry :(

Answer 13

If ABC is a secant to the circle intersecting the circle at C and B and AT is the tangent segment, then,\[\LARGE AC*AB=AT ^{2}\]

Answer 14

Theorem

If a secant segment and a tangent segment share
an endpoint outside a circle, then the product of
the length of the secant segment and the length
of its external segment equals the square of the
length of the tangent segment.

thats why AT^2 = (AC)(AB)

maybe this will help

Answer 15

but i think he needs the proof of the theorem

Answer 16

You need proof Callisto O_O

Answer 17

Nope, it's just an MC question. But I haven't learnt that before. Thanks for teaching me a new thing :)

Answer 18

welcome friend.

Answer 19

i like your question.

Answer 20

Well, if there is a proof, I would really appreciate it. But I can also do one if I have time. Thanks all :)

Answer 21

http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_CircleSecantTangent.xml

Answer 22

I learned that from this site. and wish you best of luck friend.

Answer 23

Thank you :)

Answer 24

to prove that, start by drawing BT it will form two similar triangles, then similar triangles, segments are proportional.

Answer 25

Okay, thanks again :)