1.

in the figure O is the center of the circle and OP⊥AB. If AB =8cm and OP=3cm find the diameter of the circle.

Answer»

Given :-

  • OP⊥AB
  • AB = 8CM.
  • OP = 3cm.

To Find :-

  • Diameter of circle ?

Concept USED :-

  • If a line is drawn from the centre of a circle to the chord , the the line will bisect the chord at right Angle .
  • Pythagoras Theoram .

Construction :-

Solution :-

in Right ∆OAP , we have :-

→ OP = 3cm.

→ AP = (AB/2) = (8/2) = 4cm.

So , By Pythagoras Theoram ,

→ AO = √[(3)² + (4)²]

→ AO = √[9 + 16]

→ AO = √25

→ AO = 5cm. = Radius of circle.

So,

→ Diameter of circle = 2 * Radius = 2 * 5 = 10cm. (Ans).

Hence , Diameter of Given Circle is 10cm.


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