# Math Help - circle questions

1. ## circle questions

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2. Originally Posted by dgenerationx2
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(8)

$m\widehat{BD}=50^{\circ}$

$m\widehat{CE}=90^{\circ}$

$m\widehat{DE}=360-120-50-90=100^{\circ}$

$m\angle BFC=\frac{1}{2}(m\widehat{BC}+m\widehat{DE})=\frac {1}{2}(120+100)=110^{\circ}$

3. (9)

$12x=9 \cdot 16$

$12x=144$

$x=12$

Are we to assume that the external segment of length y is a tangent to the circle? If so, use the tangent secant theorem.

$y^2=3 \cdot 27$

$y^2=81$

$y=\sqrt{81}$

$y=9$

4. (11)

$10(x+10)=8(2x+8)$

$10x+100=16x+64$

$6x=36$

$x=6$

Secant lengths are 16 and 20

thanks a lot