Triangle in a circle radius 14 cm with diameter as one side (Thales): Triangle PQR is inscribed in a circle of radius 14 cm. PQ is a diameter and PR = 10 cm. Find the area of ∆PQR.
Aptitude
Area
Difficulty: Medium
Choose an option
-
A196
-
B30√19
-
C40√17
-
D35√21
-
ENone of these
Answer
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