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Common Errors in GeometryKindly go through the article once, before solving the question or going through the solution.

Official SolutionSteps 1 & 2: Understand Question and Draw InferencesGiven that PT is a tangent to the small circle and PS is a tangent to the big circle.

ΔPTB and ΔPSA are right angled at T and S respectively.

We need to find the length of ST.

Step 3: Analyze Statement 1(1) The radii of the bigger and the smaller circles are 9 cm and 4 cm respectively.

If we drop a perpendicular BD on side AS, we get:

BDST is a rectangle (since all angles of this quadrilateral are right angles).

Therefore, since opposite sides of a rectangle are equal, SD = BT = 4 cm

This means, AD = 9 – 4 = 5cm

In right triangle ADB, by applying Pythagoras Theorem, we get:

B\(D^2\) + A\(D^2\) = A\(B^2\)

That is, B\(D^2\) = (9+4\()^2\) – (5\()^2\)

B\(D^2\) = (13+5)(13-5)

Therefore, BD = 12

Since opposite sides of a rectangle are equal, ST = BD = 12 cm

Since we have been able to determine a unique length of ST,

Statement (1) is sufficient. Step 4: Analyze Statement 2(2) PB = 52/5 cm

In right triangle BTP, we know the length of only one side: BP.

In order to find the lengths of the other sides of this triangle, we need one more piece of information – either one of the two unknown angles, or one of the two unknown sides.

Since we don’t have this information, we will not be able to find the lengths of the unknown sides of triangle BTP.

Due to a similar reasoning, we will not be able to find the length of the sides of triangle ASP.

So, we will not have enough information to find the length of ST.

Therefore statement 2 is not sufficient to arrive at a unique answer. Since we got the answer from the first statement,

Correct Answer: AThanks,

Saquib

Quant Expert

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