Question
Download Solution PDFO is the centre of this circle. Tangent drawn from a point P, touches the circle at Q. If PQ = 24 cm and OQ = 10 cm, then what is the value of OP?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
O is the centre of this circle. Tangent drawn from a point P, touches the circle at Q.
PQ = 24 cm and OQ = 10 cm
Concept used:
1. If a tangent is drawn on a circle from an external point, then at the point of tangency, it is perpendicular to the radius.
2. In a right-angled triangle, Hypotenuse2 = Base2 + Height2
Calculation:
According to the concept,
∠OQP = 90°
Hence, OP is the hypotenuse of ΔOQP which is a right-angled triangle.
Now, OP = \(\sqrt {24^2 + 10^2}\) = 26 cm
∴ The value of OP is 26 cm.
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