AB = AC = 32
SR = TR = 7
Solution:
Question 9:
Tangent theorem of a circle:
Lengths of tangents drawn from an same external point to a circle are equal.
In figure AB and AC are tangents drawn from same an external point A.
By tangent theorem of a circle,
⇒ AB = AC
[tex]\Rightarrow 2x^2=8x[/tex]
Divide both side of the equation by x.
[tex]$\Rightarrow \frac{2x^2}{x} =\frac{8x}{x}[/tex]
[tex]$\Rightarrow 2x =8[/tex]
Divide by 2 on both side of the equation.
[tex]$\Rightarrow \frac{2x}{2} =\frac{8}{2}[/tex]
[tex]$\Rightarrow x =4[/tex]
Substitute x = 4 in AB and AC.
[tex]AB=2(4)^2=32[/tex]
[tex]AC=8(4)=32[/tex]
Question 10:
By tangent theorem of a circle,
⇒ SR = TR
[tex]$\Rightarrow y=\frac{y^2}{7}[/tex]
Multiply by 7 on both side of the equation, we get
[tex]$\Rightarrow 7y =y^2[/tex]
Divide by y on both side of the equation, we get
[tex]$\Rightarrow 7 =y[/tex]
Substitute y = 7 in SR and TR
[tex]SR=y=7[/tex]
[tex]$TR=\frac{7^2}{7} =7[/tex]
