![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
As shown in the figure, in the plane rectangular coordinate system, the two sides of the rectangular oabc are respectively on the x-axis and y-axis, OA = 10 cm, OC = 6 cm, and the existing two moving points P and Q are from the As shown in the figure, in the plane rectangular coordinate system, the two sides of the rectangular oabc are respectively on the x-axis and y-axis, OA = 10 cm, OC = 6 cm. The existing two moving points P and Q start from D and a at the same time, point P moves uniformly along the direction of OA on line OA, and point Q moves uniformly along AB direction on line ab. the velocity of point P is known to be 1cm / s (1) Suppose that the velocity of point q is cm / s and the movement time is T seconds, ① When the area of △ CPQ is the smallest, find the coordinates of point Q; ② when △ cop and △ PAQ are similar, find the coordinates of point Q (2) Suppose the velocity of point q is a cm / s, ask if there is a value of a, so that △ OCP is similar to △ PAQ and △ CBQ? If so, ask for the value of a and write out the coordinates of point Q at this time; if not, please explain the reason
Question 1 Q (10,3) question 2 Q (10,3.5) and (10, - 3 + radical 39) question 2 a = Four Thirds
Known: as shown in the figure, in ⊙ o, the length of chord AB is radius OA AB and OC intersect at point P. it is proved that the quadrilateral oacb is rhombic
Prove that: ∵ C is
The midpoint of AB, OC is the radius,
∴PA=PB，AB⊥OC，
∵AP=1
2AB=
Three
2AO，
∴OP=
AO2−AP2=
AO2−3
4AO2=1
2OA=1
2OC，
∴PC=1
2oC, i.e., Op = PC,
The quadrilateral oacb is a parallelogram,
And ∵ ab ⊥ OC,
The quadrilateral oacb is rhombic
Known: as shown in the figure, in ⊙ o, the length of chord AB is radius OA AB and OC intersect at point P. it is proved that the quadrilateral oacb is rhombic
0
0
Three points a, B, C on the sphere, plane ABC and the sphere intersect in a circle, three points a, B, C on the circle
It is known that in △ ABC, ab = 12cm, BC = 18cm, CA = 24cm The longest side of another similar triangle is 36cm. Find the circumference of this triangle
Another similar longest side of the triangle corresponds to ca
36/24=1.5
So the other two sides are 18 × 1.5 = 27 12 × 1.5 = 18
Perimeter 36 + 27 + 18 = 81
As shown in the figure, BD is the angular bisector of ∠ ABC, de ⊥ AB is in E, the area of ⊥ ABC is 30cm2, ab = 18cm, BC = 12cm, then De is=______ cm．
As shown in the figure, through point D, make DF ⊥ BC, and perpendicular foot is point F
∵ BD is the angular bisector of ∵ ABC, de ⊥ ab,
∴DE=DF
The area of ABC is 30cm2, ab = 18cm, BC = 12cm,
∴S△ABC=1
2•DE•AB+1
2. DF · BC, i.e. 1
2×18×DE+1
2×12×DE=30，
∴DE=2（cm）．
Therefore, fill in 2
The lengths of the three sides of the triangle ABC are ab = 30cm, BC = 24cm, CA = 18cm. Take the midpoint D of AB and the midpoint e of BC to connect De, as shown in the right figure Calculate, measure, what proportion can you write? Even if the quantity is not enough, just write the data I gave you
15：15=12：12
15：30=12：24=9：18
A. B and C are three points on the sphere. Given the chords (the line connecting the two points on the sphere) AB = 18cm, BC = 24cm, AC = 30cm, the distance between plane ABC and the center of the ball is exactly half of the radius of the ball. The surface area and volume of the ball are calculated
Three points a, B, C on the sphere, plane ABC and the sphere intersect in a circle, three points a, B, C on the circle
In △ ABC, ab = 12cm, BC = 18cm, AC = 24cm, if △ a ′ B ′ C ′∷ ABC, and the circumference of △ a ′ B ′ C ′ is 81cm. Find the length of each side of △ a ′ B ′ C '
∵△A′B′C′∽△ABC，
The circumference of △ a ′ B ′ C ′: △ ABC perimeter = a ′ B ′: AB,
In ∵ △ ABC, ab = 12cm, BC = 18cm, AC = 24cm, and the circumference of △ a ′ B ′ C ′ is 81cm,
∴A′B′=18cm，B′C′=27cm，A′C′=36cm．
If the radius of ⊙ o is 10cm, the chord AB = 12cm, then the distance from the center of circle to AB is () A. 2cm B. 6cm C. 8cm D. 10cm
According to the vertical diameter theorem, be = 6
∵ ob = 10, ᙽ OE = 8. (Pythagorean theorem)
Therefore, C
RELATED INFORMATIONS
- 1. In circle O, the chord Mn / / EF, P is a point on circle O. the radius of circle O is known to be 10cm, Mn = 12cm, EP = 16cm. Find the distance between chord Mn and ef
- 2. As shown in the figure, in ▱ ABCD, AE bisects ∠ bad to intersect DC at point E, ad = 5cm, ab = 8cm, and calculate the length of EC
- 3. If the lengths of two parallel chords are 6cm and 8cm respectively in a circle with a radius of 5cm, the distance between the two chords is______ .
- 4. It is known that, as shown in the figure, the diameter ab of the circle O intersects with the chord CD at the point E, AE = 1, be = 5, ∠ AEC = 30 ° and find the length of CD I can't draw a picture
- 5. 0
- 6. If AB is 10, Pb is 4 and OP is 5, then find the radius of the circle
- 7. It is known that in the triangle ABC of RT, the angle ACB = 90 degrees, D and E are the midpoint of AB and BC respectively, and the point F is on the extension line of AC, and CF = De
- 8. Find a proof question: AB is the diameter of circle O, CD is a chord in the circle, AE ⊥ CD is in E, BF ⊥ CD is in F, and CE = DF
- 9. In ⊙ o, the chord ab ⊥ CD is in M. the radius of ⊙ o is 5, BM = 6, am = 2. Find the size of dm-cm
- 10. As shown in the figure, in circle O, AB is the diameter of circle O, CD is a chord, and CD is perpendicular to point P, connecting BC and AD
- 11. Given that ∠ AOB = 90 degrees, D, C divide AB into three equal parts, chord AB intersects with radius OC, OD at points E and F, and proves that AE = DC = BF
- 12. As shown in the figure, OA ⊥ OC, ob ⊥ OD, ∠ BOC = 30 ° and find AOB, COD, AOC
- 13. In the circle O, AB is the diameter, the chord CD is perpendicular to P, AC = DC = 2 times the root sign 3, and find the length of Op
- 14. As shown in the figure, ad is the diameter of ⊙ o, AC is the chord, ∠ CAD = 30 °, ob ⊥ ad is in O, AC is in B, ab = 5, and the length of BC is obtained
- 15. Circle O1 and circle O2 intersect at two points a and B, P is the point on circle O1, connecting PA and Pb, intersecting circle O2 with C and D. It is proved that po1 is perpendicular to CD
- 16. As shown in the figure, point h is the vertical center of △ ABC, the circumscribed circle ⊙ O2 of ⊙ O1 and ⊙ BCH with ab as diameter intersect at point D, and extend ad to intersect ch at point P, Verification: point P is the midpoint of Ch
- 17. As shown in the figure, circle I is the inscribed circle of the triangle ABC, which is tangent to points D, e and F with AB, BC and Ca respectively, and the angle def = 50 degrees. Find the angle A
- 18. It is known that the radii of circle O1 and circle O2 are 3cm and 5cm respectively, and if they are inscribed, the position relationship between the center of circle and O1O2? What is the positional relation? Which is the extrinsic intersection and tangent? It is known that the radius of circle O1 and circle O2 are 3cm and 5cm respectively, and if they are inscribed, the center distance of circle is 5cm!
- 19. Given that circle O1 and circle O2 are inscribed at point a, the chord ab of circle O1 intersects with circle O2 at point C, the ratio of radius of circle O1 to circle O2 is 2:3, ab = 12 emergency
- 20. The third degree of the sixth root is not equal to 5:10 of the third part of the root sign