Question: A circle is inscribed in a quadrilateral ABCD such a way that it touches all of the four sides. What is the perimeter of the quadrilateral?

(1) AB + BC = 10
(2) AB + CD = 12

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: B
Solution and Explanation:
Approach Solution 1:
This question has only 1 approach solution

The tangents drawn from any particular point the two tangents that we are talking about both will be equal. That means

If we call the points p q r s then
BP= BQ
CQ= CR
DS= DR
AP= AS

The markings in the diagram are all equal. It is asked to find the perimeter of the quadrilateral

Let's look at the statements

1. AB + BC = 10

​Breaking AB down
AP+PB
Breaking BC down
BQ+CQ

Since the sum of them is 10
So length of AP= AS and CQ becomes CR

Since the length of DR & DS are equal but we do not know them.
Therefore, statement 1 is insufficient.

2. AB + CD = 12

​Breaking AB down
AP+BP
Breaking CD down
DR+CR

AS and AP are equal
Since we know AP so we know AS
Similarly we know DR, so we know DS
Therefore, AS+DS= AD

CR is same as CQ and BP is same as BQ
Since the length is 12. Sum of the remaining length will also be 12. The perimeter is 24.
Therefore, it is sufficient.

“A circle is inscribed in a quadrilateral ABCD such a way that it touches”- is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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