Question

O is the centre of the circle and length of the chord is 8 cm seg OP _| chord AB. if l(OP)= 3cm then find the radius of the circle?​

Answer 1

Solution :-

given that,

→ O = centre of circle.

→ AB = 8 cm

→ OP ⟂ AB .

→ OP = 3 cm .

since OP is perpendicular to the chord it will bisect the chord .

So, In right angled ∆OPB, we have,

→ OP = 3 cm

→ PB = AB/2 = 8/2 = 4 cm.

→ OB = Radius of circle .

then,

→ OB² = OP² + PB² { By pythagoras theorem .}

→ OB = √(3² + 4²)

→ OB = √(9 + 16)

→ OB = √25

→ OB = 5 cm (Ans.)

Hence, the radius of the circle is equal to 5 cm .

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