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Grade 10Analytical Geometry

ina triangleabc &d on bc such that db=14,da=13 dc-4&the circum circle of adb is congruent to the circum circle of adc. what is the area of triangle abc

Profile image of srk
9 Years agoGrade 10
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1 Answer

Profile image of Vikas TU
9 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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