In the given figure, PQ is a tangent drawn at point P to a circle with center O. OQ intersects the circle at R such that OR=RQ. If PQ=3√3cm, Find the radius of the circle.
Answers
Given : PQ is a tangent drawn at a point P to a circle with centre O
OQ intersects the circle at R such that OR=RQ
PQ = 3√3cm
To Find : the radius of the circle
Solution:
OR = RQ
OQ = OR + RQ
=> OQ = OR + OR
=> OQ = 2OR
OR = OP ( Radius)
PQ is tangent
=> PQ² + OP² = OQ²
PQ = 3√3
OQ = 2OP
=> (3√3)² + OP² = (2OP)²
=> 18 + OP² = 4OP²
=> 3OP² = 18
=> OP² = 6
=> OP = √6
radius of the circle = √6
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Answer:
OR = RQ
OQ = OR + RQ
=> OQ = OR + OR
=> OQ = 2OR
OR = OP ( Radius)
PQ is tangent
=> PQ² + OP² = OQ²
PQ = 3√3
OQ = 2OP
=> (3√3)² + OP² = (2OP)²
=> 18 + OP² = 4OP²
=> 3OP² = 18
=> OP² = 6
=> OP = √6
radius of the circle = √6