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Question
PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm. A is any point on PQ. If PS = 5 cm, then ar (PAS) = 30 cm2.
Options
True
False
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Solution
This statement is True.
Explanation:
Given, PS = 5 cm
Radius of circle = SQ = 13 cm
In right-angled ΔSPQ,
SQ2 = PQ2 + PS2 ...[By Pythagoras theorem]
(13)2 = PQ2 + (5)2
⇒ PQ2 = 169 – 25 = 144
⇒ PQ = 12 cm ...[Taking positive square root, because length is always positive]
Now, area of ΔAPS = `1/2` × Base × Height
= `1/2 xx PS xx PQ`
= `1/2 xx 5 xx 12`
= 30 cm2
So, given statement is true, if A coincides Q.
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