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# Geometry Questions || Need Help ASAP please, please

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4    Hi, I need help with these asap please please. Thank you so much for your time

Mar 7, 2018
edited by Guest  Mar 7, 2018

#1
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First  one  :

A radius meeting a tangent does so at right angles.....so

angle ACB  and angle ABC  are complementary angles  in right triangle  ABC

So

24  +  angle ABC  =  90   subtract 24 from  both sides

angle ABC  =  66°

PS  - if this is from VixenGrace....I answered your other multi-part question from  yesterday.......   Mar 7, 2018
#2
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Second one :

Itersecting chord theorem :  When two chords meet in a circle.....the products of their respective individual segments are equal

This implies that

DP *  BP  = AP * PC

4 * BP  =   3.5 * 6   simplify

4 * BP  = 21   divide both sides by  4

BP =  21 / 4  =   5.25   Mar 7, 2018
#3
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Third one :

Here....I'm assuming that  YX  is tanglent to the circle

This is known as the  tangent-secant theorem....it says that

YX^2 = ZY  * VY    ....so......

YX^2   =  (28 ) * 9

YX^2  =  252        take the positive root

YX  = √ 252   =  √ [ 36 * 7  ]  =  6√7   =  15.87 m   Mar 7, 2018
#4
+1

Lastly  :

B + D   = 180

(2x + 3)  +  ( 4x + 3)  = 180

6x + 6  = 180

6x  = 174

x  =   29

So.... C  =  2*29 + 1    =   59°   Mar 7, 2018