Can you send a picture by chance?
Answer:
24
Step-by-step explanation:
LP = 15 on one side
LR= 9 on the other side
____________________|____________|
P L R
add them and PR is 24
15+9= 24
Let`s assume that points M, N and P are the touching points of those 3 circles:Then:Y M + M Z = 14,Z N + N X = 20X P + P Y = 18And also: M Z = ZN, Y M = P Y and N X = X P.Now we have a system of 3 equations ( Y M, M Z and X P are the radii of each circle ):Y M + M Z = 14M Z + X P = 20X P + Y M = 18 Y M - M Z = - 14+X P + Y M = 18 X P - M Z = 4Y M - M Z = - 14+M Z + X P = 20 X P - Y M = 6 /* ( - 1 )X P - M Z = 4 X P + Y M = - 6 X P - M Z = 4 Y M - M Z = - 2 Y M + M Z = 14 2 Y M = 12 => Y M = 6M Z - 6 = 2 => M Z = 8X P + 6 = 18
X P = 12
Radii of the circles are: 12, 8 and 6.
We have to find midpoint M of the diagonal AC (or BD, there is no difference) so:
Answer:
see explanation
Step-by-step explanation:
2 chords intersecting inside a circle , then the product of the parts of one chord is equal to the product of the parts of the other chord.
6
BE × ED = AE × CE , that is
10 × 3x = 12(2x + 1) ← distribute parenthesis by 12
30x = 24x + 12 ( subtract 24x from both sides )
6x = 12 ( divide both sides by 6 )
x = 2
then
ED = 3X = 3(2) = 6
7
RJ × JP = SJ × JQ , that is
6 × 3x = 4(4x + 1) ← distribute parenthesis by 4
18x = 16x + 4 ( subtract 16x from both sides )
2x = 4 ( divide both sides by 2 )
x = 2
then
RP = RJ + JP = 6 + 3x = 6 + 3(2) = 6 + 6 = 12
