Question 6

AB is the chord of circle of length 6 cm. From the center of the circle a perpendicular is drawn which intersects the chord at M and distance between centre and chord is 4 cm. ﬁnd the area $$(in cm^2)$$ of the circle)

Solution

Given : AB = 6 cm and OM = 4 cm

To find : Area of circle = ?

Solution : Let $$r$$ be the radius of circle

Also, MB = $$\frac{6}{2}=3$$ cm

In right $$\triangle$$ MOB,

=> $$(OB)^2=(OM)^2+(MB)^2$$

=> $$(OB)^2=(4)^2+(3)^2$$

=> $$r^2=16+9=25$$

=> $$r=\sqrt{25}=5$$ cm

$$\therefore$$ Area of circle = $$\pi r^2$$

= $$3.14 \times(5)^2=78.5$$ $$cm^2$$

=> Ans - (D)

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