    Question

# In the given figure, there are two circles that touch each other at A. P is a point which is at a distance of 25 cm from O as shown in the figure. The radius of the circle with centre O is 7 cm. The diameter of the circle with centre O’ is 10 cm. What is the length of the tangent PC? A

25 cm

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B

24 cm

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C

26 cm

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D

27 cm

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Solution

## The correct option is B 24 cm In the given figure, PO=25 cm and OA=7 cm We know that the tangent is perpendicular to the radius at the point of contact So, ∠POA=90∘. Hence, applying pythagoras theorem, we have PO2=AO2+PA2 252=72+PA2 Hence, PA2=625−49=576 ⇒PA=24 cm Now, considering the circle with centre O' alone We know that PA=24 cm. Now PA and PC are tangents from an external point P to the same circle. Hence, they are equal in length. Thus, PC=PA=24 cm.  Suggest Corrections  0      Similar questions  Explore more