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प्रश्न
In Figure 1, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC
= 4 cm, then the length of AP (in cm) is
विकल्प
A. 7.5
B. 15
C. 10
D. 9
उत्तर
AP, AQ and BC are tangents to the circle. Suppose BC touch the circle at R.
It is given that AB = 5 cm, AC = 6 cm and BC = 4 cm.
We know that, the lengths of tangents drawn from an external point to a circle are equal.
∴ AP = AQ … (1)
PB = BR … (2)
CQ = CR .... (3)
2AP = AP + AP
∴ 2AP = AP + AQ [Using (1)]
⇒ 2AP = (AB + PB) + (AC + CQ)
⇒ 2AP = (AB + BR) + (AC + CR) [Using (2) and (3)]
⇒ 2AP = AB + (BR + CR) + AC
⇒ 2AP = AB + BC + AC
⇒ 2AP = 5 cm + 4 cm + 6 cm
⇒ 2AP = 15 cm
⇒ AP = 7.5 cm
Thus, the length of AP is 7.5 cm.
Hence, the correct answer is A.
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