In fig. O is the centre of circle and, $O D = 4$ cm. If $O B = 5$ cm then the length of tangent BC is?

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Solution

The correct option is A $3$ cm
Tangent is perpendicular to radius $\Rightarrow ∠ O C B = 90^{\circ}$

$O D = O C = 4 c m$

For right-angled $Δ O C B$ ,

$O C^{2} + B C^{2} = O B^{2}$

$\Rightarrow 4^{2} + B C^{2} = 5^{2}$

$\Rightarrow B C^{2} = 25 - 16 = 9$

$\Rightarrow B C = 3 c m$

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In fig. O is the centre of circle and, OD=4 cm. If OB=5 cm then the length of tangent BC is?

The correct option is A 3 cmTangent is perpendicular to radius ⇒∠OCB=90∘ OD=OC=4cm For right-angled ΔOCB, OC2+BC2=OB2 ⇒42+BC2=52 ⇒BC2=25−16=9 ⇒BC=3cm

In fig. O is the centre of circle and, $O D = 4$ cm. If $O B = 5$ cm then the length of tangent BC is?

The correct option is A $3$ cm
Tangent is perpendicular to radius $\Rightarrow ∠ O C B = 90^{\circ}$

$O D = O C = 4 c m$

For right-angled $Δ O C B$ ,

$O C^{2} + B C^{2} = O B^{2}$

$\Rightarrow 4^{2} + B C^{2} = 5^{2}$

$\Rightarrow B C^{2} = 25 - 16 = 9$

$\Rightarrow B C = 3 c m$