Draw a circle of diameter 6cm from a point P outside the circle at a distance of 6cm from its center draw two tangents to the circle.
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Given that:
Construct a circle of radius 6 cm, and let a point P = 10 cm from its centre, construct a pair of tangents to the circle.
Find the length of the tangents.
We follow the following steps to construct the given:
Steps of construction:
1. First of all, we draw a circle of radius AB = 6 cm.
2. Make a point P at a distance of OP = 10 cm, and join OP.
3. Draw a right bisector of P, intersecting OP at Q.
4. Taking Q as center and radius OQ = PQ, draw a circle to intersect the given circle at T and T`.
5. Join PT and P`T` to obtain the required tangents.
Thus, PT and P`T` are the required tangents.
Find the length of the tangents.
As we know that OT⊥PTandΔOPT is the right triangle.
Therefore,
OT = 6 cm and PO = 10 cm.
In ΔOPT,
PT2=OP2–OT2
= (10)2–(6)2
= 100 – 36
= 64
PT = 8 cm
Thus, length of tangents = 8 cm.
Construct a circle of radius 6 cm, and let a point P = 10 cm from its centre, construct a pair of tangents to the circle.
Find the length of the tangents.
We follow the following steps to construct the given:
Steps of construction:
1. First of all, we draw a circle of radius AB = 6 cm.
2. Make a point P at a distance of OP = 10 cm, and join OP.
3. Draw a right bisector of P, intersecting OP at Q.
4. Taking Q as center and radius OQ = PQ, draw a circle to intersect the given circle at T and T`.
5. Join PT and P`T` to obtain the required tangents.
Thus, PT and P`T` are the required tangents.
Find the length of the tangents.
As we know that OT⊥PTandΔOPT is the right triangle.
Therefore,
OT = 6 cm and PO = 10 cm.
In ΔOPT,
PT2=OP2–OT2
= (10)2–(6)2
= 100 – 36
= 64
PT = 8 cm
Thus, length of tangents = 8 cm.
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