Question

24. Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it
by actual calculation,​

Answer 1

AO2 = AP2 + OP2

52 = AP2 + 4

52 = AP2 + 4

thus, AP = 4cm

Answer 2

Steps of construction :

1. Draw a circle with radius 3 cm and centre O. .

2. Draw another circle with radius 5 cm and same centre O.

3. Take a point P on the circumference of larger circle and join O to p.

4. Taking OP as diameter draw another circle which intersects the smallest circle at A and B.

5. Join A to P and B to P. Hence AP and BP are the required tangents.

Verification $\checkmark$

Using Pythagoras theoram,

OA² + AP² = OP²

AP = $\sf \sqrt{(OP² - OA²)}$

AP = $\sf \sqrt{(5² - 3²) cm}$

AP = $\sf \sqrt{4²\: cm}$

AP = 4 cm

${\boxed{\sf{Hence, verified}}}$