In the figure above, AC = 10 and ABC is a semicircle. AD = p and DC =

Question

DS21992.gif In the figure above, AC = 10 and ABC is a semicircle. AD = p and DC = q What is the ratio of the areas of triangles ABD and ABC? (1) p = 9q (2) AB = 3\sqrt{10}

the27s · Answer

Answer (C)

Area of triangle is 1/2 * b * h. 
Condition (1) gives definitive values for p,q. However, with BD being unknown, area of ABD can't be determined.
Condition (2) gives AB values, and when integrated with 'p' from condition (1), BD can be obtained. And hence areas of both triangles can be definitely computed.

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mcmoorthy · Answer

Hi the27s,

I think the answer should be A.

The question asks Area of ADB/Area of ABC.

Area of ADB = 1/2 * BD * p

Area of ABC can be split as Area of ADB + Area of DBC

Which is 1/2 * BD * p + 1/2 * BD * q

Simplifying this becomes 1/2 * BD (p +q)

Now the ratio becomes 1/2 * BD * p/(1/2*BD(p+q))

Cancelling 1/2 * BD in the numerator and denominator the ratio becomes
p/(p+q)

Now statement 1 gives p = 9q

The ratio of areas of ADB/ABC = 9q/(9q+q) = 9/10

Statement 2 : insufficient.

Answer: A

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CEdward · Answer

Tough problem. Does anyone have the answer? It says D.

CEdward · Answer

Nice. Why isn't B sufficient?

Gknight5603 · Answer

Answer is indeed D
B is also sufficient.
triangle ABD and BDC are similar.
AC 10, AB 3√10 so BC √10

By similar traingle we can calculate the height if both traingles in terms of P and Q.
thus we can get the desired area ratio

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AJ0784 · Answer

B is also sufficient. Since triangle ABD and ABC are similar, therefore the ratio of areas of these triangles is equal to the ratio of squares of the sides of these triangles.

Hence ratio of areas of ABD and ABC= (AB^2/AC^2)
Since AB=3*sqrt10 and AC=10
Therefore ratio of areas of ABD and ABC = 9/10

Therefore answer is D.

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In the figure above, AC = 10 and ABC is a semicircle. AD = p and DC =

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In the figure above, AC = 10 and ABC is a semicircle. AD = p and DC =

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