Question

Draw a circle of radius of 3 cm .draw a tangent to the circle making an angle of 30 degree with a line passing through the centre

Answer 1

Steps of construction:

Draw a circle of radius 3 cm and draw a secant PAB

Draw perpendicular bisector of PB. Let M be the midpoint of PB

With M as centre and radius MP or MB draw a semi circle

Now draw a perpendicular at point A. Let it intersect the semicircle at point C.

Measure the length PC and with P as centre and radius PC draw two arcs on the circle and mark the intersection points as T and S.

Join the points P, T and P, S.

PT and PS are the required tangents drawn from external point P.

Answer 2

Again, Steps of construction:-

Step 1:draw a circle with centre O and radius 3cm.

Step 2: Draw radius OA and produce it to B.

Step 3: Make ∠AOP = 60° .

Step 4: Draw PQ ⊥ OP , meeting OB at Q.

Step 5: Then, PQ is the desired tangent, such that ∠OQP = 30°.

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