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In a triangle ABC, take a point D on BC such that DB = 14, DA = 13, DC=4 and the circum circle of ADB is congruent to the circum circle of ADC. What is the area of triangle ABC?

Aditya Dixit , 7 Years ago
Grade 10
anser 2 Answers
Vikas TU

Last Activity: 7 Years ago

The fact that the two circumcircles are congruent means that the chord AD must subtend the same angle in both circles.
That is, ∠ABC = ∠ACB, so ABC is isosceles.
Drop the perpendicular M from A to BC;
we know MC = 9 and so MD = 5
and by Pythagoras on AMD, AM = 12.
Therefore, the area of ABC is
1/2 (AM)(BC) = 1/2 (12)(18) = 108.

satwika

Last Activity: 4 Years ago

The fact that the two circumcircles are congruent means that the chord AD must subtend the same angle in both circles.
That is, ∠ABC = ∠ACB, so ABC is isosceles.
Drop the perpendicular M from A to BC;
we know MC = 9 and so MD = 5
and by Pythagoras on AMD, AM = 12.
Therefore, the area of ABC is
1/2 (AM)(BC) = 1/2 (12)(18) = 108

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