Mathematics
The following figure shows a circle with centre O and diameter PQ. Point R lies on the circumference of the circle such that PR = QR and PR = 4 cm.
Calculate the radius of the given circle and state its value correct to two decimal places.
Circles
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Answer
Given, PQ is diameter of the circle.
PR = QR and PR = 4 cm
⇒ QR = 4 cm
As we know that,
Angle in a semi-circe is a right angle.
⇒ ∠PRQ = 90°
Triangle PQR is a right triangle with hypotenuse PQ. Using Pythagoras theorem,
⇒ PQ2 = PR2 + RQ2
⇒ PQ2 = 42 + 42
⇒ PQ2 = 16 + 16
⇒ PQ2 = 32
⇒ PQ = = 5.66 cm
Radius (OP) =
= 2.83 cm.
Hence, the radius of the given circle = 2.83 cm.
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In the following figure, O is the centre of the circle and AB is a diameter.
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