Explain (Question:366635.0)

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TRINA DAS

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· 1 Months ago

Explain (Question:366635.0)

Explain the last line of solution in detail.

Question:

In the given figure, $Δ$ PQR is drawn such that PQ is tangent to a circle whose radius is 10 cm. QR passes through centre of the circle. Point R lies on the circle. If QR=36 cm, then what is the area (in $c m^{2}$ ) of $Δ$ PQR.

Options:

134.5

148

166.15

180

Solution:

$\begin{matrix} Q O = Q R - O R = 36 - 10 = 26 c m, \\ P Q = \sqrt{O Q^{2} - O P^{2}} = \sqrt{2 6^{2} - 1 0^{2}} = 24 c m \\ I n Δ O P Q, \\ s i n (O Q P) = \frac{O P}{O Q} = \frac{10}{26} = \frac{5}{13} \\ A r e a o f Δ P Q R = \frac{1}{2} \times Q P \times Q R \times s i n (P Q R) = \frac{1}{2} \times 24 \times 36 \times \frac{5}{13} = 166.15 \end{matrix}$

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