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8.1 Voltooi die volgende: Die oorstane hoek van h koordvierhoek is … (1) 8.2 In die diagram, is EF en EG raaklyne aan die sirkel met middelpunt O - NSC Mathematics - Question 8 - 2016 - Paper 2
Question 8
8.1 Voltooi die volgende: Die oorstane hoek van h koordvierhoek is … (1) 8.2 In die diagram, is EF en EG raaklyne aan die sirkel met middelpunt O. FH || EK, EK sny ... show full transcript
Worked Solution & Example Answer:8.1 Voltooi die volgende: Die oorstane hoek van h koordvierhoek is … (1) 8.2 In die diagram, is EF en EG raaklyne aan die sirkel met middelpunt O - NSC Mathematics - Question 8 - 2016 - Paper 2
Step 1
FOGE is koordvierhoek is.
Answer
To show that FOGE is a cyclic quadrilateral, we need to prove that the opposite angles are supplementary. Since EF is a radius of the circle, and EG is also a radius, we have:
- Angle EFO = 90° (angle at radius and tangent)
- Angle EGO = 90° (angle at radius and tangent)
Thus, we have:
This confirms that FOGE is a cyclic quadrilateral.
Step 2
EG h raaklyn aan sirkel GJK is.
Answer
To show that EG is a tangent to circle GJK, we can use the property that the angle between a tangent and the radius at the point of contact is 90°.
Since FH is parallel to EK (given) and we have:
- Angle G1 = Angle H = x (corresponding angles)
- Angle R1 = R1 (Equal segments)
This implies that EG meets circle GJK at a right angle. Hence, EG is a tangent to the circle.
Step 3
FEG = 180° - 2x.
Answer
For the angle FEG:
Given that angles FEG and EHG are angles in the cyclic quadrilateral FOGE, and the angles in a cyclic quadrilateral are supplementary, we can state:
- Angle FEG + Angle EHG = 180°
- We already established that Angle EHG = 2x (since angle at the circle subtends the same arc)
Thus:
This completes the proof.