The circle, center Q has diameter AB.The circle intersects BP at N.
Triangle BMQ is mapped onto triangle BMA by an enlargement, scale factor= 2.
Given that QM= 3 cm
1) show that MN= 6 cm
2) find MC
Figure attached!

Question

The circle, center Q has diameter AB.The circle intersects BP at N. 
Triangle BMQ is mapped onto triangle BMA by an enlargement, scale factor= 2. 
Given that QM= 3 cm
1) show that  MN= 6 cm
2) find MC 
Figure attached!

anonymous · Answer

attachment

anonymous · Answer

Uh. Sorry. It's BNA.

experimentx · Answer

any other parameter given??

experimentx · Answer

R??

experimentx · Answer

BM must be equal to MN

anonymous · Answer

since <BNA is right(90º) triangle , <BMQ = <ANP.  It is becouse the segment crossing at right angle form same angles between them. In this case BA _ AP and BN AN. Next:
It means NP = MQ =3. Since scale factor is 2, AN =6, and again since  <BMQ = <ANP, BM =6. Now becouse of scale factor , BN = 12 and so  MN =6. The part 2 you do the same way, by observing that <BAP = <CBQ

experimentx · Answer

NP = MQ =3??

anonymous · Answer

<BMQ = <ANP

experimentx · Answer

how ??? i thought they were just similar

anonymous · Answer

1º:
QN || AN
so BN perpendicular to AN.
2º BA perpendicular AP
it means angle at A equals angle at B. And since this are right triangles it means all angles will be the same, o..... triangles are equal

experimentx · Answer

that gives you two triangles are similar ... not congruent

experimentx · Answer

you need to prove at least one side is equal

experimentx · Answer

i think at least one parameter is missing.  If ABCD is a square then, it can be proved that those two triangles are congruent/

experimentx · Answer

and rest is like you said.

anonymous · Answer

You right, my mistake, but i have another way, :)

anonymous · Answer

If ADBC would be square its easy.
 actualy all the triangles that you find visualy on the picture have a congruent one :)

experimentx · Answer

yep ... somewhat seems to me like this http://i.stack.imgur.com/d6n4Z.gif

experimentx · Answer

http://i.stack.imgur.com/JKISK.png

anonymous · Answer

Thank you @experimentX and @myko. These were all the values that were given in the question. ABCD is a a square. 
I understood the way you did it, BTW! :) Thank you!

experimentx · Answer

If it's a square ... Prove that QBC and BAP are congruent triangles
prove BMQ and ANP are similar triangles
=> they will have equal area /// so they must be congruent (similar plus equal)
=> rest is same as myko did above