powerprep - arc

Question

Please provide some explaination to this/ Thanks

jimmylow · Answer

Triangle PQR is a right triangle, So are triangle PQT and triangle QRT (where T is perpendicular to Q on line / diameter a-b)

Statement (1) gives a = 4. Since 2 is proportion to 4, then b = 1/2 * 2 = 1. Thus, a = 4, b = 1. a+b = 5. Sufficient. Eliminate B,C,E.

Statement (2) gives b = 1. Since b is proportion to 2, then a = 2 * 2 = 4. a+b = 5. Sufficient. Eliminate A.

Ans: D.

alimad · Answer

Jimmy bear with me as I try grasping the concept.

Can you go into the elements of these statements please :

Statement (1) gives a = 4. Since 2 is proportion to 4, then b = 1/2 * 2 = 1. Thus, a = 4, b = 1. a+b = 5. Sufficient. Eliminate B,C,E.

Statement (2) gives b = 1. Since b is proportion to 2, then a = 2 * 2 = 4. a+b = 5. Sufficient. Eliminate A.

jimmylow · Answer

Alimad
These two diagrams should make my explanation clearer. Detach the smaller right triangle and place it on the bigger right triangle. You will see the values falling in place and my answer per above.

alimad · Answer

excellent. Thanks

manojrana9 · Answer

To prove that a is proportional to QT (2), the two triangles- PQT & QTR need to be similar.

Angle PQT & Angle TQR need to be equal. How do you prove that??

jimmylow · Answer

Here is the answer to Mano's question.

We know the x + y deg in right triangle PQR = 90 deg. For right triangle QRT, given that we know y deg on long leg, the opposite is x deg. For right triangle PQT, given that we know x deg, then the opposite is y deg.

Thus, we know that right triangle PQT and right triangle QRT have similar x and y deg angles. :-D

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