draw a circle of a radius 3cm.from a point 6cm away from its centre construct the pair of tangents to the circle and measure their lengths
Answers
Answered by
9
Steps of construction:-
1. Draw a circle of radius 3cm with centre O.
2. A point P was marked outside the circle such that, OP = 6cm.
3. P to O was joined.
4. Perpendicular bisector of PO was found to be M.
5. With MO as radius and M as center a circle was drawn touching the previous drawn circle.
6. Point of intersections of two circles were marked to be Q and R respectively.
7. P was joined to Q and R respectively.
Therefore, required tangents will be PQ and PR.
In ΔPQO, if <Q= 90° then,
PO x PO = PQ x PQ + QP x QP
=> PO x PO - QP x QP = PQ x PQ
=> 6 x 6 - 3 x 3 = PQ x PQ
=> 36 - 9 = PQ x PQ
=> √27 = PQ
=> 3√3 cm = PQ
Hence, length of both tangents which are here equal to 3√3cm.
Similar questions