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Re: In the figure, ABC and ADC are right triangles. Which of the [#permalink]
Expert Reply
In the case AC is the hypotenuse of the triangle, we have by The Pythagorean Theorem, \(AC^2 = AD^2 + DC^2\)

\(5^2 = AD^2 + DC^2\)

This equation is satisfied by III since \(5^2 = 1^2 + (\sqrt{24})^2\) .

Therefore, III is possible.

Hope is more clear now to you Sir.

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Re: In the figure, ABC and ADC are right triangles. Which of the [#permalink]
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JelalHossain wrote:
Can someone please explain C (especially IV option) is correct ? Thank you


The trick here is to recognize that the right angle in triangle ACD could be in 3 different places.
∠CAD could be 90°
∠CDA could be 90°
∠DCA could be 90°

Cheers,
Brent
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Re: In the figure, ABC and ADC are right triangles. Which of the [#permalink]
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JelalHossain
Please notice that there is a perpendicular sign. Which means <ABC = 90°. So, AC is the hypotenuse. But, there is no perpendicular sign on the other side. We do not know which side is the hypotenuse. Therefore, we can say that AC^2 + CD^2 = AD^2 or CD^2 + AD^2 = AC^2 or AD^2 + AC^2= CD^2. III & IV satisfy the equation. That makes C the right answer.
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