Geo 3

[yellowho]

Triangle/Circle Problem:

[maihuna]

connect C towards the line length 5 meeting circle: let it be D, we know CD will be perpendicular to BD, so RT anfle Triangle ADC with measurement : X, 2, 4, where 4 will be hyp so x = (4^2-2^2)^1/2 = 2(3)^1/2

[Anurag@Gurome]

Refer to the above figure.
N is the center of the semicircle.
As Ab is a tangent to the circle at point M, NM is perpendicular to AB.

Now, ∆ABC and ∆ANM are similar because,

• Angle A is common in both
  angle M = angle C = Right angle

Hence, NM/BC = AN/AB ................................................ (1)

Now, NM = CN = radius of the semicircle = r (say)
Hence, AN = AC - CN = (4 - r)
And, BC = 3, AB = 5

Replacing these values in (1),

• .... r/3 = (4 - r)/5
  => 5r = 12 - 3r
  => 8r = 12
  => r = 12/8 = 3/2 = 1.5

Hence, radius of the semicircle is 1.5

[Anurag@Gurome]

connect C towards the line length 5 meeting circle: let it be D, we know CD will be perpendicular to BD

No, it won't.
C is not the center of the semicircle.