Question

Find the length of the tangent drawn to a circle of radius 3 cm,from a point at a distance 5 cm from the centre.
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Answer 1

Answer:

As we know that the focal length of a spherical mirror is equal to half the radius of curvature of that mirror. So, according to your question the radius of curvature of a convex mirror is 32cm. 16 cm. So the focal length of the convex mirror is 16cm

Answer 2

Draw a circle, taking C as centre and radius CT = 3 cm

Let PT be the tangent, drawn from point P to a circle with centre C

Let CP = 5 cm

CT = 3 cm (given)

∠CTP = 90⁰ (since radius is perpendicular to tangent)

From △CPT,

CP² = PT² + CT² (By Pythagoras theorem)

(5)² = PT² + (3)²

We get,

PT² = 25 – 9

PT² = 16

PT = √16

We get,

PT = 4

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