As shown in the figure, it is known that AB is the diameter of ⊙ o, AC is the chord, and bisection ⊥ bad, ad ⊥ CD, and the perpendicular foot is d Proof: CD is tangent of ⊙ o

As shown in the figure, it is known that AB is the diameter of ⊙ o, AC is the chord, and bisection ⊥ bad, ad ⊥ CD, and the perpendicular foot is d Proof: CD is tangent of ⊙ o

Proof: OA = OC,
∴∠OCA=∠OAC；
∵ AC bisection ∠ bad,
∴∠OAC=∠CAD，
∴∠OCA=∠CAD；
⊥ CD ⊥ i.e,
∴∠OCA+∠DCA=90°，
⊥ OC ⊥ CD, that is, CD is the tangent line of ⊙ o

The diameter ab of the circle O is known, and the vertical chord CD at point e passes through C as the tangent CG of circle O. the extension line of AB intersects the point C and extends the intersection ad to point F and

Area of part

As shown in the figure, AB is the diameter of semicircle o, passing through point o as the perpendicular line of chord ad, the tangent line AC at point C, OC and semicircle o at point E, connecting be and de (1) It is proved that: ∠ bed = ∠ C; (2) If OA = 5, ad = 8, find the length of AC

(1) It is proved that ∵ AC is tangent of ⊙ o, AB is ⊙ o diameter,
∴AB⊥AC．
Then ∠ 1 + ∠ 2 = 90 °,
And ∵ OC ⊥ ad,
∴∠1+∠C=90°，
∴∠C=∠2，
Bed = ∠,
∴∠BED=∠C；
(2) Connect BD,
∵ AB is ⊙ o diameter,
∴∠ADB=90°，
∴BD＝
AB2−AD2＝
102−82＝6，
∴△OAC∽△BDA，
∴OA：BD=AC：DA，
That is, 5:6 = AC: 8,
∴AC=20
3．

As shown in the figure, point d moves on the chord ab of ⊙ o, ab = 4, connecting OD, making the vertical line of OD intersect ⊙ o at point C, then the maximum value of CD is______ .

When the center of the triangle is 2, the maximum OCD can be obtained
Therefore, when AB is the diameter and D is the midpoint of AB, the maximum value of CD is obtained, which is half of ab. because AB = 4, the maximum value of CD is 2,
So the answer is 2

As shown in the figure, AB is the diameter of circle O, AC is the chord, D is the midpoint of AC, BC = 8cm, and the length of OD is calculated Sorry, I don't want you to use your intelligence

Because AB is the diameter of the circle
So 2ao = ab
And D is the midpoint of AC
So 2ad = AC
Dao = cab
So triangle Dao is similar to triangle cab
So 2od = BC = 8cm
OD=4

As shown in the figure, AB is the diameter of ⊙ o, AC is the chord, and D is the midpoint of AC. if od = 4, find BC

∵ AB is the diameter of ⊙ o, AC is the chord, D is the midpoint of AC,
∴AD=CD，OA=OB，
That is, OD is the median line of △ ABC,
∴BC=2OD=2×4=8．

As shown in the figure, we know that AB is the diameter of ⊙ o, point D is the midpoint of chord AC, BC = 8cm, and find the length of OD

∵ point O is the midpoint of AB and point D is the midpoint of chord AC,
The OD is the median line of △ ABC,
∴OD=1
2BC=4cm．

As shown in the figure, AB is the diameter of ⊙ o, AC is the chord, and D is the midpoint of AC. if od = 4, find BC

∵ AB is the diameter of ⊙ o, AC is the chord, D is the midpoint of AC,
∴AD=CD，OA=OB，
That is, OD is the median line of △ ABC,
∴BC=2OD=2×4=8．

The radius of a circle is expanded by three times, its circumference is expanded by () times, and its area is expanded by () times Writing analysis

The circumference C = 3.14159 * 2R R is expanded by 3 times, which is 4 times of the original, that is, the circumference is expanded to 4 times and expanded 3 times
The area is s = 3.14159 * R ^ 2, R is expanded by 3 times, that is, R ^ 2 = 16, so the area is expanded to 16 times and expanded by 15 times

A circle has a radius of 2 cm, and its circumference and area are equal

Wrong, the unit is not sample, not comparable