In the circle given below, let OA =1 unit, OB =13 unit and PQ perp OB. Then, the area of the triangle PQB (in square units) is

Question

In the circle given below, let OA =1 unit, OB =13 unit and PQ perp OB. Then, the area of the triangle PQB (in square units) is <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/809634727d1d4945cae28501d020e4cb-.png" /> (A) 24 √2 (B) 24 √3 (C) 26 √3 (D) 26 √2

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/eae58ee4287304c8eeb96be1de3129a1-.png" /> PA = AQ =λ OA ⋅ AB = AP ⋅ AQ ⇒ 1.12=λ . λ ⇒ λ=2 √3 Area Δ PQB =(1/2) × 2 λ × AB Δ=(1/2) ⋅ 4 √3 × 12 =24 √3

Q. In the circle given below, let $O A = 1$ unit, $OB = 13$ unit and $PQ ⊥ OB$ . Then, the area of the triangle $PQB$ (in square units) is

$242$

$243$

$263$

$262$

$P A = A Q = λ$
$O A \cdot A B$
$= A P \cdot A Q$
$\Rightarrow 1.12 = λ . λ$
$\Rightarrow λ = 23$
Area $Δ PQB = \frac{1}{2} \times 2 λ \times A B$
$Δ = \frac{1}{2} \cdot 43 \times 12$
$= 243$

Q. In the circle given below, let OA=1 unit, OB=13 unit and PQ⊥OB. Then, the area of the triangle PQB (in square units) is

242​

243​

263​

262​