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 (2x^2)/(x) =(8x)/(x)`

`$\Rightarrow 2x =8`

Divide by 2 on both side of the equation.

`$\Rightarrow (2x)/(2) =(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=(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=(7^2)/(7) =7`