Answer:
.
See the diagram attached below.
Let the chords be AB and AC with common point A.
AD is the diameter. Join B with D and C with D to form two triangles.
We need to prove that AB=AC.
\begin{gathered}In\ \triangle ABD\ and \triangle ACD;\\Given\ that\ \angle BAD=\angle CAD----(condition\ 1)\\since\ AD\ is\ diameter, \angle ABD=\angle ACD = 90^0\\So\ \angle ADB=\angle ADC--------(condition\ 2)\\AD=AD\ (common\ side)-----(condition\ 3)\\ \\So\ the\ triangles\ are\ congruent\ by\ ASA\ rule.\\Hence\ AB=AC.\end{gathered}
In △ABD and△ACD;
Given that ∠BAD=∠CAD−−−−(condition 1)
since AD is diameter,∠ABD=∠ACD=90
0
So ∠ADB=∠ADC−−−−−−−−(condition 2)
AD=AD (common side)−−−−−(condition 3)
So the triangles are congruent by ASA rule.
Hence AB=AC.
Answer:
what do you need help with?
Step-by-step explanation:
0.6 miles.
Since there is 0.8 miles to hike in total, she hiked 0.2 miles.
To solve, we just easily subtract the amount that Liz hiked from the amount that needs to be hiked.
She hiked 0.2 miles, which means we need to subtract 0.2 from 0.8.
8 - 2 = 6
The answer is 0.6 miles.
Answer:
x = 2 cm
y = 2 cm
A(max) = 4 cm²
Step-by-step explanation: See Annex
The right isosceles triangle has two 45° angles and the right angle.
tan 45° = 1 = x / 4 - y or x = 4 - y y = 4 - x
A(r) = x* y
Area of the rectangle as a function of x
A(x) = x * ( 4 - x ) A(x) = 4*x - x²
Tacking derivatives on both sides of the equation:
A´(x) = 4 - 2*x A´(x) = 0 4 - 2*x = 0
2*x = 4
x = 2 cm
And y = 4 - 2 = 2 cm
The rectangle of maximum area result to be a square of side 2 cm
A(max) = 2*2 = 4 cm²
To find out if A(x) has a maximum in the point x = 2
We get the second derivative
A´´(x) = -2 A´´(x) < 0 then A(x) has a maximum at x = 2
