Maths-
General
Easy
Question
A Chord of length 16 cm is at a distance of 6 cm from the centre of the circle. Calculate the radius of the circle?
Hint:
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
If a is the perpendicular, b is the base, and c is the hypotenuse, then according to the definition, the Pythagoras Theorem formula is given as
c2= a2 + b2
The correct answer is: Hence, the radius of the circle is 10 cm.
Given the length of the chord as 16 cm.
We know that a line from the centre of the circle perpendicular to the chords bisects the chord. So, BD = 8 cm. Also, AB is the radius, angle ADB is the right angle and AD is the distance of the chord from the centre i.e. AD = 6 cm.
Applying Pythagoras theorem to △ADB
AB2 = AD2 + BD2
AB2 = 62 + 82
AB2 = 100
AB = 10 cm
Final Answer:
Hence, the radius of the circle is 10 cm.
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