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Construction of Tangents to a Circle from a Point outside the Circle

Draw a tangen...

Question

Draw a tangent to the circle with centre O, and radius 3.3 cm from a point A such that d(O,A) = 7.5 cm. Measure the length of tangents segments.

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Solution

Steps of construction:
1. Draw a circle of radius 3.3 cm with centre O. Take a point A such that OA = 7.5 cm.
2. Obtain the midpoint M of seg OA.
3. Draw a circle taking M as centre and OM as the radius.
4. Let P and Q be the points of intersection of these two circles.
5. Draw rays AP and AQ which are the required tangents. When measured, AQ = 6.6 cm.

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