# The areas of two sectors of two different circles with equal corresponding arc lengths are equal. Is this statement true? Why

**Solution:**

Take two __circles__ of radii r_{1}, r_{2} or arc length l_{1}, l_{2} and θ_{1}, θ_{2} as the __corresponding angles__ of sectors

l_{1} = r_{1}θ_{1} π/180

l_{2} = r_{2}θ_{2} π/180

It is given that

l_{1} = l_{2}

r_{1}θ_{1} = r_{2}θ_{2} = x

Take A1 and A2 as the __area of sector__

A_{1} = πr_{1}^{2}θ1/360

A_{2} = πr2^{2}θ2/360

Let us divide A_{1} by A_{2}

\(\frac{A_{1}}{A_{2}}=\frac{\frac{\pi r_{1}\Theta _{1}r_{1}}{360^{0}}}{\frac{\pi r_{2}\Theta _{2}r_{2}}{360}}\) = xr1/xr2 = r1/r2

A_{1}/A_{2} = r_{1}/r_{2}

Here

Area of sector can be equal when r_{1}/r_{2} = 1

Area of sectors of two circles of same arcs length are not equal

Therefore, the statement is false.

**✦ Try This:** In a circle, an arc of length 4π cm subtends an angle of measure 40°

at the centre. Find the radius of the circle and the area of the sector corresponding to that arc.

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 12

**NCERT Exemplar Class 10 Maths Exercise 11.2 Problem 9**

## The areas of two sectors of two different circles with equal corresponding arc lengths are equal. Is this statement true? Why

**Summary:**

The statement “The areas of two sectors of two different circles with equal corresponding arc lengths are equal” is false

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