Triangle in a circle radius 14 cm with diameter as one side (Thales):\nTriangle PQR is inscribed in a circle of radius 14 cm. PQ is a diameter and PR = 10 cm. Find the area of ∆PQR.

Difficulty: Medium

196
30√19
40√17
35√21
None of these

Correct Answer: 30√19

Explanation:

Introduction / Context:
By Thales’ theorem, an angle subtended by a diameter is a right angle. Thus ∆PQR is right-angled at R with hypotenuse PQ = diameter = 28 cm.

Step-by-Step Solution:

PR = 10; PQ = 28; let QR = x.By Pythagoras: 10^2 + x^2 = 28^2 ⇒ x^2 = 784 − 100 = 684 ⇒ x = √684 = 2√171 = 6√19.Area = (1/2) * PR * QR = 0.5 * 10 * 6√19 = 30√19.

Final Answer:
30√19

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