radious of two concentric circle are 13 and 8.AB is diameter of circle with larger radius .BD thouches a circle with smaller rediusat D find AD.
Answers
Step-by-step explanation:
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Reference of Image is in the attachment :
Join OD, and OD will be Radius of Smaller Circle and Perpendicular to the Tangent BD
∴ ∠ ODB = 90° ⠀[ Perpendicular ]
AB is Diameter, and P is point on the Semi Circle. Angle in a Semi Circle is Right Angle.
∴ ∠ APB = 90° ⠀[ Angle in Semi Circle ]
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Now, we will Similar the Triangles.
• In Triangle APB and, Triangle OBD :
⇒ ∠ APB = ∠ ODB ⠀⠀—( Both are 90° )
⇒ ∠ ABP = ∠ OBD ⠀⠀—( Common Angle )
∴ ∆ APB ~ ∆ OBD ⠀⠀—( AA Similarlity )
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• Sides of Similar Triangles are Proportional
⇒ AP /OD = AB /OB
⇒ AP /8 cm = 26 cm /13 cm
AB is Diameter of Large Circle
⇒ AP /8 cm = 2
⇒ AP = 2 × 8 cm
⇒ AP = 16 cm
∴ Therefore, Value of AP will be 16 cm.