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Q.

ABC is any triangle inscribed in the circle x2+y2=r2 such that A is fixed point. If the external and internal bisectors of ∠A intersect the circle at D and E, respectively, then which of the following statements is true about ∆ADE?

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a

Its centroid is a fixed point.

b

Its circumcentre is a fixed point.

c

Its orthocentre is a fixed point.

d

none of these

answer is A.

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Detailed Solution

Orthocentre of ∆ADE is A itself and its circumcentre is at origin. Hence, centroid is also a fixed point.
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ABC is any triangle inscribed in the circle x2+y2=r2 such that A is fixed point. If the external and internal bisectors of ∠A intersect the circle at D and E, respectively, then which of the following statements is true about ∆ADE?