Question

Draw a circle of radius 2.5 cm. Take a point a part 6.5 cm from its center and from this point draw the tangents to the circle. Measure the length of tangent also find the length of tangents by calculation.

Answer 1

Steps of construction :

(1) First of all, we draw a circle with center O and radius 2.5 cm

(2) Take a point P a part 6.5 cm from the center of circle and join OP.

(3) Draw a perpendicular bisector of PO and mark the point M.

(4) Taking M as center and radius and draw a circle which intersects their circle center O at A and B.

(5) Join PA and PB.

Hence PA and PB are the required tangents.

On measuring we get PA = PB = 6.0 cm.

Calculation to find the length of tangents :

In ∆POA

∠PAO = 90°

So ∆POA is a right angled triangle, 

So by the Pythagoras Theorem,

PO² = AO² + PA²

⇒ PA² = PO² – AO²

= (6.5)² – (2.5)²

= 42.25 – 6.25

⇒ PA² = 36.00

∴ PA = \(\sqrt { 36 }\) = 6 cm

Hence, the length of each tangent is 6.0 cm.