'p' is any exterior point of circle and AP, BP are tangents to circle. A,B are any two points on the circle if AP = 24cm then PB = __________.
(A) 5cm
(B) 25cm
(C) 24cm
(D) 13cm
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Answers
Answer:
13 cm
Step-by-step explanation:
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Answer:
The length of the segment PB is 24 cm.
Option C) 24 cm
Step-by-step-explanation:
NOTE: Refer to the attachment for the diagram.
In figure, we have given that,
O is the centre of circle.
P is an exterior point of circle.
Segments PA and PB are tangents to the circle.
AP = 24 cm
Now,
Join seg OA, OB and OP. - - - [ Construction ]
Now, we know that,
Tangents drawn to a circle are perpendicular to the radius of the circle.
∴ Seg PA ⊥ Seg OA - - - ( 1 )
Also,
Seg PB ⊥ Seg OB - - - ( 2 )
Now, in △OAP & △OBP,
Seg OA ≅ Seg OB - - - [ Radii of the same circle ]
∟OAP ≅ ∟OBP - - - [ From ( 1 ) & ( 2 ) ]
Seg OP ≅ Seg OP - - - [ Common side ]
∴ △OAP ≅ △OBP - - - [ Hypotenuse - side test ]
∴ Seg AP ≅ Seg BP - - - ( 3 ) [ c. s. c. t. ]
Now,
AP = 24 cm - - - [ Given ]
∴ Seg BP = Seg AP = 24 cm - - - [ From ( 3 ) ]
∴ The length of the segment PB is 24 cm.
