23 uždavinys

Taškas C priklauso pusapskritimiui su centru O.  AB ⊥ CD, AD = 4, DB = 9. Apskaičiuokite atkarpos CD ilgį.

Sprendimas.

AB = AD + DB = 4 + 9 = 13.

AO = AB / 2 = 6.5

OC = AO = 6.5.

DO = AO - AD = 6.5 - 4 = 2.5.

Pagal pitagoro teoremą $$OC^{2} = DO^{2}+CD^{2}$$.

$$CD = \sqrt {OC^{2}-DO^{2}}$$

saknis( 6.5^²- 2.5^²)  = 

saknis( 6.5^²- 2.5^²) = $$\sqrt {6.5^{2}-2.5^{2}}$$ = 

$${\normalsize 6.5^{2}}$$ = $${\normalsize 42.25}$$

saknis(42.25- 2.5^²) = $$\sqrt {42.25-2.5^{2}}$$ = 

$${\normalsize 2.5^{2}}$$ = $${\normalsize 6.25}$$

saknis(42.25-6.25) = $$\sqrt {42.25-6.25}$$ = 

$${\normalsize 42.25-6.25}$$ = $${\normalsize 36}$$

saknis(36) = $$\sqrt {36}$$ = 

$${\normalsize \sqrt {36}}$$ = $${\normalsize 6}$$

6$$6$$

$$\sqrt {6.5^{2}-2.5^{2}}$$  = $$$$

$$\sqrt {42.25-6.25}$$  = $$$$

$$\sqrt {36}$$  = $$$$

$$6$$ $$$$

saknis(6.5^2-2.5^2)  = 

saknis(42.25-6.25)  = 

saknis(36)  = 

6

Atsakymas: 6