Question

15 points!!! GEOMETRY help please!!
Questions attached!

Answer 1

7.

`\text{If the line segment labeled 6 is tangent to the circle then is rectangle triangle.}\\\\\text{ We can use Pythagorean theorem.}`


`x^2=2.5^2+6^2\\x^2=6.25+36\\x^2=42.25\\x=√(42.25)\\x=6.5\\\\Answer:\boxed{6.5}`

8.

`\text{If BC is tangent to circle then m}\angle OBC=90^o`


`\text{We can use the converse of Pythagorean theorem}`


`8\ and\ 12\\\\8^2+12^2=20^2\\64+144=400\\208=400\ -FALSE\\\\8;\ 4√(21)\\\\8^2+(4√(21))^2=20^2\\64+16\cdot21=400\\64+336=400\\400=400\ -O.K.\\\\12\ and\ 14\\\\12^2+14^2=20^2\\144+196=400\\340=400\ -FALSE\\\\10\ and\ 10\sqrt3\\\\10^2+(10\sqrt3)^2=20^2\\100+100\cdot3=400\100+300=400\\400=400\ -O.K.\\\\14\ and\ 4√(51);\ 4√(51) > 20 - FALSE`

`\text{because the line segment labeled 20 is the longest side of the triangle}`



`Answer:\ \boxed{8\ and\ 4√(21);\ 10\ and\ 10\sqrt3}`