Grade 10Analytical Geometry

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

9 Years agoGrade 10

2 Answers

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.

satwika

5 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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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

2 Answers

Vikas TU

satwika

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