Construct two concentric circles with centre O with radii 3 cm and 5 cm. Construct tangent to a smaller circle from any point A on the larger circle. Measure and write the length of tangent segment. Calculate the length of tangent segment using Pythagoras theorem.. Created by simranjeetr53019.

Construct two concentric circles with centre O with radii 3 cm and 5 cm. Construct tangent to a smaller circle from any point

Answer:

Following are the steps to draw tangents on the given circle:

Draw a circle of 3 cm radius with centre O on the given plane.

Draw a circle of 5 cm radius, taking O as its centre. Locate a point P on this circle and join OP.

Bisect OP. ...

Taking M as its centre and MO as its radius, draw a circle. ...

Join PQ and PR.

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Answer:

AQ and AP are the required tangent and length of the tangent are 4cm each .

Step-by-step explanation:

Explanation:

Given , radii of the two concentric circles are 3cm and 5 cm .

By using ruler and compass we draw two concentric circles with centre O and radii 3cm and 5 cm .

Step 1:

Let A as a centre take more than half of length AO draw an arcs
Similarly , from point O take more than half of length AO draw an arcs which cut the previous arcs .
Now , join the point where they intersect .
Plot M which is mid point of AO .
Draw a another circle of radius AM .
Now plot Q and P where the new circle intersect the smaller circle whose radius is 3cm
Join QA and PA .

Hence , this is our required diagram and AQ and AP are tangent .

Step 2:

Now join OP and we know that tangent to a circle is perpendicular to the radius at the point of tangency.

∴ In right angle triangle Δ APO ,

OP = 3cm , AO = 5cm

By Pythagoras theorem we have ,

[tex]AO^{2} = AP^{2} +OP^{2}[/tex]

⇒[tex]5^{2} = AP^{2} + 3^{2}[/tex]

⇒ AP = [tex]\sqrt{25 - 9 } = \sqrt{16}[/tex] = 4 cm .

Final answer:

Hence , the length of tangent is 4 cm .

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