(Q9) Draw a circle of radius 6cm. From a point 10 cm away from its center, construct the pair of tangents to the circle and measure their lengths.Verify by using pythagoras Theorem.

Steps of construction:

  1. Draw a circle with center 'O' and radius 6cm.
  2. Take a point P outside the circle such that OP = 10cm. Join OP.
  3. Draw the perpendicular bisector OP which bisects it at M.
  4. Taking M as center and PM or MO as radius draw a circle.Let the circle intersects the given circle at A and B
  5. Join P to A and B
  6. PA and PB are the required tangents of lengths 8cm each.
ABYP

Proof: In △OAP

OA2+AP2 = 2+2

= + =

OP2 = 2 =

OA2+AP2 = OP2

Hence AP is a tangent

Similarly BP is a tangent