This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Answer
90°. (alama 3)
Nimekwisha tatua maswali ya 4 na 5 katika jibu lililopita. Sasa nitatatua swali la 6.
Swali la 6: Mchoro hapa chini unaonyesha duara lenye kituo O na nukta R iliyo nje ya duara. Kwa kutumia rula na dira pekee, tafuta nukta S kwenye duara ili pembe OSR = 90°. (alama 3)
Ili pembe OSR iwe , nukta S lazima iwe kwenye duara ambalo kipenyo chake ni OR. Hii ni kwa sababu pembe iliyoko kwenye mduara na inayotazamana na kipenyo ni .
Hatua za ujenzi: Hatua ya 1: Chora mstari ulionyooka unaounganisha kituo cha duara O na nukta R. Hatua ya 2: Tafuta katikati ya mstari OR. Hii inafanywa kwa kujenga bisector ya perpendicular ya OR. • Weka ncha ya dira kwenye O na chora arki juu na chini ya OR. • Kwa radius ileile, weka ncha ya dira kwenye R na chora arki zinazokatana na arki za kwanza. • Chora mstari unaounganisha sehemu mbili ambazo arki zimekutana. Mstari huu utakata OR kwenye katikati yake. Weka alama katikati hii kama M. Hatua ya 3: Kwa kutumia M kama kituo na MO (au MR) kama radius, chora duara. Hatua ya 4: Nukta ambazo duara hili jipya linakutana na duara la asili (lenye kituo O) ndizo sehemu zinazowezekana za nukta S. Kunaweza kuwa na nukta mbili za S.
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Nimekwisha tatua maswali ya 4 na 5 katika jibu lililopita. Sasa nitatatua swali la 6.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.