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.
ScanSolve AI Answer
Haya! Hapa kuna masuluhisho ya maswali yako: Swali la 24: a) Urefu wa kamba ya kawaida AB. Kutokana na data, tuna duara mbili zenye vituo O na Q, na radii r = 8 cm. Umbali kati ya vituo OQ = 12 cm. Kamba ya kawaida AB hukutana na OQ kwa X. OQ ni bisector ya perpendicular ya AB. Katika OAX, OA = 8 cm. Wacha OX = x na AX = y. Katika QAX, QA = 8 cm. Wacha QX = 12 - x. Kutumia theorem ya Pythagoras: Katika OAX: OA^2 = OX^2 + AX^2 8^2 = x^2 + y^2 64 = x^2 + y^2 (i) Katika QAX: QA^2 = QX^2 + AX^2 8^2 = (12-x)^2 + y^2 64 = (12-x)^2 + y^2 (ii) Kutoa (i) kutoka (ii): 0 = (12-x)^2 - x^2 0 = (144 - 24x + x^2) - x^2 0 = 144 - 24x 24x = 144 x = (144)/(24) = 6 cm Sasa badilisha x=6 katika (i): 64 = 6^2 + y^2 64 = 36 + y^2