If P, Q and R are the areas of sectors at A, B and C within the triangle respectively, then which of the following is/are correct?<br><br>1. P=\pi\text{ cm}^{2}<br>2. 9Q+4R=36\pi\text{ cm}^{2}<br><br>Select the correct answer using the code given below :
Consider the following for the next three (03) items that follow: ABC is a triangle with sides AB=6\text{ cm}, BC=10\text{ cm} and CA=8\text{ cm}. With vertices A, B and C as centres, three circles are drawn each touching the other two externally.
- A. 1 <strong>ONLY</strong>
- B. 2 <strong>ONLY</strong>
- C. Both 1 and 2 ✓
- D. Neither 1 nor 2
Correct Answer: C. Both 1 and 2
Explanation
Solving for radii gives r_a=2, r_b=4, r_c=6. Since \angle A = 90^{\circ}, area P = \frac{90^{\circ}}{360^{\circ}}\pi(2)^2 = \pi, so 1 is correct. Areas Q = \frac{B}{360}\pi(4)^2 and R = \frac{C}{360}\pi(6)^2. Thus, 9Q+4R = \frac{144\pi}{360}B + \frac{144\pi}{360}C = \frac{144\pi}{360}(B+C). Since B+C = 90^{\circ}, 9Q+4R = \frac{144\pi}{360} \times 90 = 36\pi. Both are correct.
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