Question

In the above figure ,O is the centre of the circle ,P is the midpoint of chord AB. If l(AB)=80 cm, l(OB)=41 cm, then find l(OP).​

Answer 1

Answer:

By pygos theorem,

l(OB)² = l(OP)² + l(PB)²

(41)² = l(OP)² + l(40)²

SO, l(OP)² = (41)² - (40)²

= 1681 - 1600

= 81

l(OP) = root of 81

l(OP) = 9 cm.

Answer 2

$\boxed{\huge{\red{\mathfrak{Answer}}}}$

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Bisected cord are perpendicular to center .

So, Angle P → 90°

PB → 40 cm

OB → 41 cm

In right ∆ OPB , Right angled at P ,

So, by Pythagoras Theorm ,

OP → $\sqrt{{41}^{2}-{40}^{2}}$

OP → $\sqrt{1681-1600}$

OP → $\sqrt{81}$

OP → $\mathtt{\huge{9\:cm}}$

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