Using ruler and a compass only, construct a semi-circle with diameter BC = 7 cm. Locate a point A on the circumference of the semi-circle such that A is equidistant from B and C. Complete the cyclic quadrilateral ABCD, such that D is equidistant from AB and BC. Measure `angleADC` and write it down.

Answer

### Step-by-Step Solution:

**Step 1: Draw the Diameter BC**
- Using a ruler, draw a line segment BC that measures 7 cm. Label the endpoints as B and C.

**Hint:** Use a ruler to measure exactly 7 cm for the diameter.

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**Step 2: Find the Midpoint O**
- Find the midpoint O of the line segment BC. Since BC is 7 cm, O will be at 3.5 cm from either B or C.

**Hint:** The midpoint is calculated by dividing the length of the segment by 2.

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**Step 3: Draw the Semicircle**
- With O as the center and OB (or OC) as the radius (3.5 cm), use a compass to draw a semicircle above the line segment BC.

**Hint:** Ensure the compass is set to the correct radius before drawing the semicircle.

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**Step 4: Locate Point A**
- Since point A needs to be equidistant from B and C, it should lie directly above O on the semicircle. Mark this point A.

**Hint:** A point directly above the midpoint of the diameter in a semicircle is always equidistant from the endpoints of the diameter.

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**Step 5: Draw Lines AB and AC**
- Connect points A to B and A to C using a ruler to form the triangle ABC.

**Hint:** Ensure that the lines are straight and accurately connect the points.

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**Step 6: Locate Point D**
- To find point D, which is equidistant from lines AB and AC, draw the angle bisector of angle BAC. This will intersect the semicircle at point D.

**Hint:** The angle bisector can be constructed using a compass and straightedge by finding equal angles from point A to lines AB and AC.

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**Step 7: Complete the Cyclic Quadrilateral ABCD**
- Connect point D to points B and C to complete the cyclic quadrilateral ABCD.

**Hint:** Ensure that all points are connected accurately to form the quadrilateral.

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**Step 8: Measure Angle ADC**
- Use a protractor to measure the angle ADC. Record the measurement.

**Hint:** Extend line AD if necessary to measure the angle accurately.

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### Final Measurement:
- The measure of angle ADC is found to be 135 degrees.

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