if the angle between two tangents draw from an external point P to a circle of radius a and centre O, is 90degree,then find the length of OP
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The length OP is units.
- Let the two tangents drawn from an external point P to the circle be PQ and PR.
- Given,
O is center of the circle with radius a.
OQ = OR = a
∠QPR = 90°
- OP is the angle bisector of ∠QPR
⇒ ∠OPQ = ∠OPR = 45°
- We know that, the tangent drawn to a circle is perpendicular to radius.
⇒ ∠OQP = ∠ORP = 90°
- Now, ΔOPQ is a right angled triangle
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