In die diagram is COD die middellyn van die sirkel met middelpunt O - NSC Mathematics - Question 10 - 2024 - Paper 2
Question 10
In die diagram is COD die middellyn van die sirkel met middelpunt O. EA is 'n raakyln aan die sirkel by F. AO ⊥ CE. Middellyn COD is verleng om die raakyln aan die s... show full transcript
Worked Solution & Example Answer:In die diagram is COD die middellyn van die sirkel met middelpunt O - NSC Mathematics - Question 10 - 2024 - Paper 2
Step 1
10.1 TODF 'n koordvierhoek is
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Answer
Gegewe dat ar{O}_1 = 90^ ext{o} en ar{F}_1 + ar{T}_1 = 90^ ext{o}. Die hoeke in 'n semi cirkel is regshoekig.
Daarom is TODF 'n koordvierhoek.
Step 2
10.2 $ar{D}_B = ar{T}_I$
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Answer
Die opposisie hoeke van die vierhoek is gelyk volgens die eienskap van 'n koordvierhoek.
ar{B}_2 = ar{T}_1.
Step 3
10.3 ΔTFO || ΔDFE
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Answer
Aangesien ar{D}_B = ar{T}_I, volg dit dat die twee driehoeke saamgestelde hoeke het.
Daarom, ΔTFO en ΔDFE is parallel.
Step 4
10.4 Indien $ar{B}_2 = ar{E}_1$, bewys dat DB || EA.
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As ar{B}_2 = ar{E}_1, dan is die besit van gelyke hoeke te danke aan die opposisie van die korrespondensie van die hoeke.
Daarom is DB || EA.
Step 5
10.5 Bewys dat DO – TO.FE / AB.
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Answer
In ΔABD, die eienskap van linies wat aan die een kant van 'n lyn parallel is aan 'n ander lyn impliseer.
