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प्रश्न
In the following figure, AP, AQ and BC are tangents of the circle with centre O. If AB = 5 cm, AC = 6 cm and BC = 4 cm, then the length of AP (in cm) is
पर्याय
15
10
9
7.5
MCQ
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उत्तर
7.5
Explanation:
Perimeter of ΔABC = AB + BC + AC
= AB + BR + RC + AC
= (AB + BP) + (CQ + AC) ...[∵ BD = BQ, CD = CQ, (tangents from external points)]
= AP + AQ
= 2AP ...[∵ AP = AQ, tangents from external point]
∴ AB + BC + AC = 2AP
⇒ 5 + 4 + 6 = 2AP
⇒ AP = `15/2`
⇒ AP = 7.5 cm
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