Question 1152378


given: {{{AB = 5.5}}}, {{{CD = 7}}}, and {{{FE = 19.5}}}

If two segments from the same exterior points are tangent to a circle, then they are congruent. Since {{{AF}}} and {{{AB }}}are segments from the same exterior point ({{{A}}}), then

{{{ AB = AF }}} and {{{AF = 5.5}}}

 Since {{{CB}}} and {{{CD}}} are segments from the same exterior point ({{{B}}}), then

 {{{CD = CB}}} and {{{CB = 7}}}

Since {{{EF}}} and {{{ED}}} are segments from the same exterior point ({{{E}}}), then 

{{{FE = DE}}} and  {{{DE= 19.5}}}

{{{AE = AF + FE}}}
{{{AE = 5.5 + 19.5}}}
{{{AE = 25}}}

{{{CE = CD + DE}}}
{{{CE = 7 + 19.5}}}
{{{CE = 26.5}}}

Therefore, 
{{{AE = 25}}} and {{{CE = 26.5}}}


Question 9

If {{{BD = 2.4}}} and {{{AB = 1.0}}}, calculate the value of {{{DA}}}.

circle {{{D}}} with tangent line segment {{{AC}}} touching at point{{{ B}}}; line segment {{{AD}}}

If a line is tangent to a circle, then it is perpendicular to the radius, making {{{ABD}}} a right triangle.
Since you have to calculate {{{DA}}}, use the Pythagorean Theorem. 

{{{(AB)^2+ (BD)^2= (AD)^2}}}
{{{(1.0)^2+ (2.4)^2= (AD)^2}}}
{{{1+ 5.76= (AD)^2}}}
{{{6.76= (AD)^2}}}
{{{AD=sqrt(6.76)}}}
{{{AD=2.6}}}


Question 10
If {{{AB = 9}}}, {{{CD = 12}}}, and {{{FE = 22}}}, calculate the values of line segment {{{AE}}} and line segment {{{CE}}}
image of a circle inscribed inside triangle {{{ACE}}}; the points of intersection points are: on side {{{AC}}} point {{{B}}}, on side {{{AE}}} point {{{F}}}, and on side {{{CE}}} point {{{D}}}

Tangents to a circle from the same point are the same length, so 

  {{{FA = AB = 9}}}

  {{{AE = FA +FE = 9 +22 = 31}}} 
and,

  {{{DE = FE = 22}}}

  {{{CE = CD +DE = 12 +22 = 34}}}

The side lengths are 

{{{AE = 31}}}, {{{CE = 34}}}


Question 11

What is true about the construction of a regular hexagon inscribed in a circle?



answer:

The circle intersects each vertex of the hexagon.


Question 12.

Which of the following shows a circle passing through three non-collinear points, A, B, and C?


One and only one circle can be drawn through A, B, and C

answer: circle circumscribed about triangle


Question 13
Which of the following is true about the following construction of a tangent to a circle from a point outside of the circle?



Since the construction of the tangent of a circle from a point outside the circle is given by the following steps:

Draw a line connecting the point to the center of the circle.
 Construct the perpendicular bisector of that line.
Place the compass on the midpoint, adjust its length to reach the end point, and draw an arc across the circle .
Where the arc crosses the circle will be the tangent points.
Hence from the first step we get a line segment {{{OB}}}.

now from the second step we get a perpendicular bisector of line {{{OB}}} at point {{{M}}}.

This means that {{{OM=MB}}} ( since bisector means that the line is cut into two equal parts)

Hence, option: {{{B}}} is correct.

answer:  {{{OM=MB}}}