Tangents/circular theorem question unit 1 GMA

[mikehepro]

Started doing GMA hw on tangents and circular theorem and I'm struck. Could anyone please show me the solutions to these 3 questions? Any help would be greatly appreciated. Thank you.

[Daenerys Targaryen]

For the first question:
You know that from the middle of the circle to the tangent makes a right angle. (radii and tangent)
We can also find the distance between the two corners in which the block and circle touches the ground:
i.e pythag of ; where c is that distance
We can also find the angle this 'c' makes with the tangent
i.e

Now imagine a triangle being formed from the vertices of 'c' to the origin
The angles in which are the same are now 90 - 'what ever we found the inverse tan of'
Having found the angle within that triangle, you can use the sin rule for the radius

[Phy124]

For the first question:
You know that from the middle of the circle to the tangent makes a right angle. (radii and tangent)
We can also find the distance between the two corners in which the block and circle touches the ground:
i.e pythag of ; where c is that distance
We can also find the angle this 'c' makes with the tangent
i.e

Now imagine a triangle being formed from the vertices of 'c' to the origin
The angles in which are the same are now 90 - 'what ever we found the inverse tan of'
Having found the angle within that triangle, you can use the sin rule for the radius

Alternatively, let's say that the circle has equation with it's centre at

The point that the corner of the box touches the circle is or for simplicity's sake.

Put these values into your original equation:





edit: Spelling

[mikehepro]

Thx for the help.
I tend to use the XPxPY=APxBP
Therefore I get 10PY=28x28
PY= 784/10
PY=78.4
78.4+10 = 88.4 which is the diameter
And I divide that by half and got 44.2cm is that good or u reckon I'm better off with Ur way phy, thanks

[Phy124]

Nice work, looks good to me.

Whichever method is the most efficient for you is the one you should use

I never studied GMA or Spesh so I do most problems using methods knowledge, possibly giving an alternate interpretation and method to most

[mikehepro]

Right and I got the answers to the last 2 too, thanks guys for the help.