How would you use the following figure to justify the statement that the angle in a semicircle is 90°? Class 9
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How would you use the following figure to justify the statement that the angle in a semicircle is 90°? Class 9
Question 1.
How would you use the following figure to justify the statement that the angle in a semicircle is 90°? Class 9
Solution:
OA = OP = OQ ...[Given]
∆OAP is an isosceles triangle.
∴ ∠OAP = a
... [sides opposite to equal sides]
Similarly, ∠OAQ = b
∠PAQ = ∠PAO + ∠OAQ
= a + b
In ∆PAQ,
∠APQ + ∠PQA + ∠PAQ = 180°
... [Angle sum property]
∴ a + b + (a + b) = 180°
∴ 2 (a + b) = 180°
∴ a + b = 90°
∴ ∠PAQ = 90°
∴ Angle in a semicircle is 90