A point Q is 13 cm from the centre of a circle. The length

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A point Q is 13 cm from the centre of a circle. The length of the tangent drawn from Q to a circle is 12 cm. The distance of Q from the nearest point of the circle is

1. 7 cm
2. 8 cm
3. 5 cm
4. 12 cm

Correct Option: B

According to question , we draw a figure of a circle with centre O

Here ,QB = Tangent = 12 cm.
OQ = 13 cm.
∠QBO = 90°
From ∆ OQB,
OB = √OQ² - QB²
OB = √13² - 12² = √169 - 144
OA = OB = √25 = 5 cm.
∴ AQ = Shortest distance = OQ – OA = 13 – 5 = 8 cm.