Math Question involving tangents of a circle

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1

<p>Could someone please explain the following: </p>

<p>College Board SAT Skills Insight for Math Band Score 700-800: </p>

<p>Skill Group 9 (Question 1) sat.collegeboard.com/practice/sat-skills-insight/math/band/700/skill/9</p>

<p>Skill Group 8 (Question 1) sat.collegeboard.com/practice/sat-skills-insight/math/band/700/skill/8</p>

<p>Skill Group 5 (Question 3) sat.collegeboard.com/practice/sat-skills-insight/math/band/700/skill/5</p>

<p>Thank you!</p>

2

<p>The first question you have to realize that this is a right angled triangle because the line segment QR is tangent to the circle forming a ninety degree angle at R. PR is a radius length 6 units. and PQ are the to radii together so 6+1= 7, now you need to find RQ by Pythagorean theorem PQ^2-PR^2=RQ^2 = 7^2 - 6^2 = 13, so PQ = the square root of 13, RS is equal to RQ - QS so square root of 13 - 1(radius)</p>

3

<p>I know tangent is it touches in 1 point but I think all you really need to know is that it forms a triangle. PQ is 7, PR is 6, then do pythagorean to find RQ and subtract 1 to get RS.</p>

<p>If it’s divided by 10 and the remainder is 9 then you know the ones digit has to be a 9. Example 19 divided by 10 you get 1 remainder 9.</p>

<p>If it’s divided by 9 you get a remainder 8. If you divide 9 by 9 you get remainder 0. 19 by 9 you get remainder 1. 29 by 9 you get remainder 2. The remainder is equal to the 1s digit. So if you want a remainder 8 you’re tens digit has to be 8 so your number is 89.</p>

<p>89 divided 10 = 8 remainder 9
89 divided by 9 = 9 remainder 8</p>

<p>I’m not sure if there’s a better way to do it but that’s how I saw it.</p>

<p>For the last one visualize a large triangle and you have to find its altitude. First split it in half vertically. The hypotenuse would be the length of 2 radiuses so it’s 8. The lower leg has a value of 4. It’s a 30 60 90 triangle so the longer leg would have a value of 4 radical 3. So now to get the length of h you just add 8, 4 from the top circles and 4 from the bottom circle to complete your line. Sorry if its not too clear but I think you could understand it after reading this and looking at the picture.</p>

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<p>This is how I do the second question… n/10=9 n/9=8, so 9 19 and 17 respecitvely… the first will always have 9 as the units digit, so keep adding 9 to the outcome of 17 till you reach 89 (i do it on my calculator)</p>

5

<p>The last one… you have to realize that those points form a triangle… cut the triangle into half so it’s going to be a right angled triangle… hypotenuse 8 and the other side is a radius so 4… 8^2 - 4^2 = 48… so now you know that the third side is 4 root 3… then you add the left over part above and below the side which are two radii so 4root3 + 8 :)</p>

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<p>I probably skipped steps in the last question… :slight_smile: I think I should make it more clear. :slight_smile: please wait for my following explanation.</p>

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<p><a href=“http://imageshack.us/photo/my-images/718/mathquestion.png/[/url]”>http://imageshack.us/photo/my-images/718/mathquestion.png/&lt;/a&gt;&lt;/p&gt;

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<p>@NaderMekadis & Brolex
Thank you soo much! This was really great help. I took forever figuring these 3 out. Really, thank you! :)</p>