Geometry Problem. Post your solution in the comment box below.

Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

## Saturday, February 3, 2018

### Geometry Problem 1353: Tangent Circles, Perpendicular Diameters, Congruence, 30 Degrees

Labels:
30 degrees,
angle,
circle,
congruence,
diameter,
perpendicular,
tangent

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https://photos.app.goo.gl/zWeKMpDAXjawGeye2

ReplyDeleteLet r and R are radius of circles A and B

Draw HP ⊥DH and NI ⊥ to DC ( see sketch)

In right triangle DHP we have DH^2=DB. DP

In right triangle DGC we have BG^2= DB. BC

So FG^2=4. BG^2= DB.(4BC)

Since FG=DH => DP=4.BC= 4.R

Since NC // HP So DN/DH= DC/DP=2r/(4R)=NI/BH=NI/R => NI=1/2.r

Triangle AIN is 30-60-90 degrees triangle.

So ∠ (MCN)=1/2 ∠ (MAN)= 30 degrees