Class 10th circle chapter example

. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle. Answer: Draw the diagram as shown below.  Here, AB is the tangent that is drawn on the circle from a point A. So, the radius OB will be perpendicular to AB i.e. OB ⊥ AB We know, OA = 5cm and AB = 4 cm Now, In △ABO, OA2 =AB2+BO2 (Using Pythagoras theorem) 52 = 42+BO2 BO2 = 25-16 BO2 = 9 BO = 3 So, the radius of the given circle i.e. BO is 3 cm. 7. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle. Answer: Draw two concentric circles with the center O. Now, draw a chord AB in the larger circle which touches the smaller circle at a point P as shown in the figure below.  From the above diagram, AB is tangent to the smaller circle to point P. ∴ OP ⊥ AB Using Pythagoras theorem in triangle OPA, OA2= AP2+OP2 52 = AP2+32 AP2 = 25-9 AP = 4 Now, as OP ⊥ AB, Since the perpendicular from the center of the circle bisects the chord, AP will be equal to PB So, AB = 2AP = 2×4 = 8 cm So, the length of the chord of the larger circle is 8 cm

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