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The base BC of DeltaABC is fixed and the...

The base BC of `DeltaABC` is fixed and the vertex A moves, satisfying the condition `cot.(B)/(2) + cot.(C)/(2) = 2 cot.(A)/(2)`, then

A

`b + c = a`

B

`b + c = 2a`

C

vertex A moves along a straight line

D

vertex A moves along an ellipse

Text Solution

Verified by Experts

The correct Answer is:
B, D
Given `(s(s-b))/(Delta) + ((s-c))/(Delta) = (2s(s-a))/(Delta)`
`rArr s-b + s - c = 2 (s-a)`
`rArr b+c = 2a`
So, locus of vertex A is an ellipse
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CENGAGE-PROPERTIES AND SOLUTIONS OF TRIANGLE-Exercise (Multiple)
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  10. A circle of radius 4 cm is inscribed in DeltaABC, which touches side B...

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  11. If H is the orthocentre of triangle ABC, R = circumradius and P = AH +...

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  12. Let ABC be an isosceles triangle with base BC. If r is the radius of t...

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  14. The area of a regular polygon of n sides is (where r is inradius, R is...

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  15. In acute angled triangle A B C ,A D is the altitude. Circle drawn with...

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  16. If A is the area and 2s is the sum of the sides of a triangle, then

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