Question

In the given figure, PQR is a triangle in which PQ = PR. A circle is drawn which passes through Q and touches PR at S and intersects PQ at T. If S is the mid-point of PR and PT = 4.5 cm, then length of PQ is

• A.
  9 cm
• B.
  13.5 cm
• C.
  18cm
• D.
  22.5 cm

Answer 1

The correct option is C

18cm

Given that PQ = PR, S is the mid-point of PR and PT = 4.5 cm.

Apply Tangent-Secant Theorem,

$PT\times PQ=P{S}^2\Rightarrow 4.5\times PQ={\left(\frac{PQ}{2}\right)}^2(\because PS=\frac{PR}{2}andPR=PQ)\Rightarrow 4.5\times PQ=\frac{P{Q}^2}{4}\Rightarrow PQ=18cm$

Hence, the correct answer is option c.