Mathematics
In the given diagram, the radius of the circle with centre O is 3 cm. PA and PB are the tangents to the circle which are at right angle to each other. The length of OP is:
cm
3 cm
cm
cm
Circles
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Answer
Join OA and AP.
Given,
Radius of circle (OB) = 3 cm
PB and AP are at right angles.
We know that,
Radius and tangent at point of contact are perpendicular to each other.
OA ⊥ AP
From figure,
⇒ OA = OB = 3 cm [Radius of circle]
⇒ OB is perpendicular to PB
⇒ ∠OBP = 90°
This shows APBO is square.
OA = PB = AP = OB = 3 cm.
In right angled triangle OBP,
⇒ OP2 = OB2 + PB2
⇒ OP2 = 32 + 32
⇒ OP2 = 9 + 9
⇒ OP2 = 18
⇒ OP =
⇒ OP = cm.
Hence, option 3 is the correct option.
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Reason (R): The total surface area of two hemispheres together is equal to the surface area of the original sphere.
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