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Q 1. The in-radius of an equilateral triangle is of length {tex} 3 \mathrm { cm } . {/tex} Then the length of each of its medians is
{tex} 12 \mathrm { cm } {/tex}
{tex} \frac { 9 } { 2 } \mathrm { cm } {/tex}
{tex} 4 \mathrm { cm } {/tex}
{tex} 9 \mathrm { cm } {/tex}
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Q 2. If the orthocentre and the centroid of a triangle are the same, then the triangle is :
Scalene
Right angled
Equilateral
Obtuse angled
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Q 3. If {tex} \mathrm { ABC } {/tex} is an equilateral triangle and {tex} \mathrm { D } {/tex} is a point on {tex} \mathrm { BC } {/tex} such that {tex} \mathrm { AD } \perp \mathrm { BC } , {/tex} then
{tex} A B: B D = 1: 1 {/tex}
{tex} A B: B D = 1: 2 {/tex}
{tex} A B: B D = 2: 1 {/tex}
{tex} A B: B D = 3: 2 {/tex}
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Q 4. In a triangle, if orthocentre, circumcentre, incentre and centroid coincide, then the triangle must be
obtuse angled
isosceles
equilateral
right-angled
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Q 5. If {tex} \mathrm { ABC } {/tex} is an equilateral triangle and {tex} \mathrm { P } {/tex},{tex} \mathrm { Q } ,\mathrm R{/tex} respectively denote the middle points of {tex} \mathrm { AB } , \mathrm { BC } , \mathrm { CA } {/tex} then.
{tex}\mathrm{PQR}{/tex} must be an equilateral triangle
{tex} \mathrm { PQ } + \mathrm { QR } + \mathrm { PR } = \mathrm { AB } {/tex}
{tex} \mathrm { PQ } + \mathrm { QR } + \mathrm { PR } = 2 \mathrm { AB } {/tex}
{tex}\mathrm{PQR}{/tex} must be a right angled triangle
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Q 6. Let {tex}ABC{/tex} be an equilateral triangle and {tex}AX, BY, CZ{/tex} be the altitudes. Then the right statement out of the four given responses is
{tex} A X = B Y = C Z {/tex}
{tex} A X \neq B Y = C Z {/tex}
{tex} A X = B Y \neq C Z {/tex}
{tex} A X \neq B Y \neq C Z {/tex}
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Q 7. If the three medians of a triangle are same then the triangle is
equilateral
isosceles
right-angled
obtuse-angle
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Q 8. Let {tex}G{/tex} be the centroid of the equilateral triangle {tex}ABC{/tex} of perimeter {tex} 24 \mathrm { cm } . {/tex} Then the length of {tex}AG{/tex} is
{tex} 2 \sqrt { 3 } \mathrm { cm } {/tex}
{tex} \frac { 8 } { \sqrt { 3 } } \mathrm { cm } {/tex}
{tex} 8 \sqrt { 3 } \mathrm { cm } {/tex}
{tex} 4 \sqrt { 3 } \mathrm { cm } {/tex}
