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2020 HKDSE Math Paper 2 Q40: Circle and Exponential Functions

2020 HKDSE Math Paper 2 Q40: Circle and Exponential Functions
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2020-05-19 18:51
CircleFunctionCoordinate Geometry
This example demonstrates the 2020 Hong Kong Diploma of Secondary Education (HKDSE) Mathematics Paper 2 Question 40, involving circles, exponential functions, and coordinate geometry. It shows how to solve problems related to circles and exponential functions by constructing circles, plotting exponential function graphs, calculating distances and angles. GeoGebra commands used include Intersect, Circle, Segment, Angle, Distance, etc. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. Intersect(AngularBisector[e, b], AngularBisector[d, b]) → I
  2. Intersect(e, d) → A
  3. Intersect(d, b) → B
  4. Intersect(e, b) → C
  5. Circle(I, Distance[I, d]) → c
  6. Intersect(c, d, 1) → E
  7. Segment(I, E) → r
  8. Angle(A, E, I) → α
  9. Intersect(c, b, 1) → D
  10. Distance(I, A) → f

AI Drawing Prompt Reference

Draw a circle tangent to two lines that intersect with a third line, forming a triangle. Start by drawing three lines: two intersect at a point, and the third crosses both, creating three vertices. Construct the angle bisectors of the angles formed by the two lines with the third line; their intersection is the circle's center. Use the distance from this center to one of the lines as the radius to draw the circle, which touches two of the lines. Mark the tangency point on one line and the intersection of the circle with the other line. Connect the center to the tangency point)Skip, and measure the distance from the center to one triangle vertex. Finally, indicate the angle at the tangency point between the center, the tangency point, and the vertex.
The prompt above was compiled from the original drawing commands and is for reference only.