Question

I really need help if I fail this test I fail my grade so please help!!?

Answer 1

`TH=3`

Explanation:

It's on Yahoo Answers:

`GA` is the diameter of the circle `T`.

Therefore`TA, TB, TD, TF, TG` are all radii of this circle and have a length of `5cm` as given in the question.

It is also given that `TD` (radius) is perpendicular to `BF` (chord). This automatically means that `BF` is bisected since it is perpendicular to the radius.

So as a result, `BH = FH = 1/2 xx BF = 4`.

Also, since `TD` is perpendicular to `BF`, that means we can look at triangle `THB`, where angle `THB = 90°`.

Apply Pythagorean theorem:

(`BH)^2 + (TH)^2 = (TB)^2`

`4^2 + (TH)^2 = 5^2`

`(TH)^2 = 25-16=9`

`TH = sqrt9=3`

You can solve for `TH`, or recognize this is a 3-4-5 triangle.

`TH = 3`

Answer 2

`TH=3`
`TL=7.9`

Explanation:

Where your question read 'BE' I think that should be 'BF'

`TA=5` and is a radius, `TB =5` as it too is a radius.

When a line from the centre meets a chord at `90°`, it bisects the chord. So when `TH` meets `BF` it bisects it making `BH=4`

`TBH` is a right angled triangle where the hypotenuse is `5`, one side is `4` so use Pythagoras to find the missing side `TH`

`5^2-4^2=TH^2`
`25-16=TH^2`
`TH=sqrt9 =3`

On the second question, `TL` is a radius and `ML` is a tangent so they meet at `90°`.

So `TML` is a right angled triangle so again use Pythagoras;

`12^2-9^2=TL^2`
`144-81=TL^2`
`TL=sqrt63`
`TL=7.937253933`