Question

I don't know how to answer number 9 and 10. Can someone please help me?

Answer 1

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

$\Rightarrow 2x^2=8x$

Divide both side of the equation by x.

$\Rightarrow \frac{2x^2}{x} =\frac{8x}{x}$

$\Rightarrow 2x =8$

Divide by 2 on both side of the equation.

$\Rightarrow \frac{2x}{2} =\frac{8}{2}$

$\Rightarrow x =4$

Substitute x = 4 in AB and AC.

$AB=2(4)^2=32$

$AC=8(4)=32$

Question 10:

By tangent theorem of a circle,

⇒ SR = TR

$\Rightarrow y=\frac{y^2}{7}$

Multiply by 7 on both side of the equation, we get

$\Rightarrow 7y =y^2$

Divide by y on both side of the equation, we get

$\Rightarrow 7 =y$

Substitute y = 7 in SR and TR

$SR=y=7$

$TR=\frac{7^2}{7} =7$