volume one
I. Multiple choice questions/kloc-0 1.C2.C3.C4.A5.B6.B
Fill in the blanks. Tangency 8. 9. Tangent 10.2 or 8.
1 1. 12.
Third, answer questions.
13. solution: the distance from the center of point a to the straight line BC is
,
∴ When the radius is r = 3 and r < D, the straight line BC is out of the circle;
When the radius r = 4 = d, the straight line BC is tangent to the circle;
When the radius r = 5 >; D, the straight line BC intersects the circle.
14. The radii of the two circles are 5cm and 2cm respectively.
15. Proof: If AO and CO are connected, then ∠ACO =∠CAO, ∠ AOC = 2 ∠ B.
∵∠ACO + ∠CAO + ∠AOC = 180? .
∴2∠CAO + 2∠B = 180? . ∴∠CAO + ∠B = 90? .
∠∠CAE =∠b,∴∠CAO+∠CAE = 90? .
∴OA⊥AE is at point A.∴AE, O is tangent to point A.
16.( 1) Sketch.
(2) If ⊙O' and OB are tangent to point E and ⊙O is tangent to point G, then O, O' and point G are on the same straight line, and ∠O'OE = 45? .
Connection Ⅷ
∴ in Rt△O'OE,
Solution,
∴ The maximum cutting radius is10cm.
Volume b
First, multiple-choice questions 1. B 2。 A 3。 C
Fill in the blanks. Tangency is 5.45 or 135 6.5.
Third, answer questions.
7. Solve the equation and get.
When a straight line intersects a circle; When, the straight line is separated from the circle.
8. solution: AC = AF.
Proof: When connecting OO' and extending it, its extension line must pass through G point and connect O'F,
Then there is O'F⊥AB.
Let OA = R and the radius of ⊙O' be R.
In Rt△OFO.
That is to say, ∴.
∴ .
In Rt△AOC, OA = OC = R,
∴AC=,∴AC = AF。 Let O'E = r, then O'O = 4-r, O'E⊥OE.