The best way to do this is to draw a picture of ΔFKL and include line segment KM that is perpendicular to FL. This creates ΔFKM which is a 45°-45°-90° triangle and ΔLKM which is a 30°-60°-90° triangle.
Find the lengths of FM and ML. Then, FM + ML = FL
<u>FM</u>
ΔFKM (45°-45°-90°): FK is the hypotenuse so FM =
<u>ML</u>
ΔLKM (30°-60°-90°): from ΔFKM, we know that KM =
, so KL =
<u>FM + ML = FL</u>

= 
Answer:
3a) The value of x = 56
3b) The measure of ∠ H T M = 90°
3c) The radius of the circle = 53
Step-by-step explanation:
3a) ∵ A F is a tangent to the circle O at point F
∵ Secant AH intersects circle O at point T
∴ (A F)² = (A T)(A H)
∴ 7( x + 7) = (21)² ⇒ ÷ 7
∴ x + 7 = 63
∴ x = 63 - 7 = 56
3b) ∵ HM is a diameter
∴ The measure of the arc HM = 180° ⇒ semi-circle
∵ ∠ H T M is inscribed angle subtended by the arc HM
∴ m ∠ H T M = half the measure of arc HM
∴ m ∠ H T M = 180° ÷ 2 = 90°
3c) ∵ Δ H T M is a right angle triangle at T
∴ (H M)² = (M T)² + (H T)² ⇒ Pythagorean theorem
∴ (H M)² = (90)² + (56)²
∴ (H M)² = 11236
∴ HM =
= 106
∴ OM = 106 ÷ 2 = 53
∵ OM is the radius of the circle O
∴ The radius = 53
Answer:Number Sets. There are sets of numbers that are used so often they have special names and symbols: ... The numbers you can make by dividing one integer by another (but not dividing by zero). In other words ... If you square a real number you always get a positive, or zero, result. ... x + 7 = 0, x = −7, Integers, set integer.
Step-by-step explanation:
To figure out this question, I first divided 24 into 3, which gives me an answer of 8. then I divided 52 into 7 , which also is 8 . because the two numbers are the same, I know the ratios are equivalent.
I hope this helps you
x =4
f (4)= 4.4+7 = 16+7=23
f (4)= 4.4-7=16-7=9