Question

if ab is a tangent drawn from a point P to a circle with Centre c and radius 1.5 centimetres that angle ACB is equal to 30 degree then find the length of a tangent AB
and a line CB ​

Answer 1

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cb = 3 cm   & ab = 3√3/2  cm If ab is a tangent drawn from an point b to a circle with centre c and radius 1.5 cm sucb that angle cba=30 degree

Step-by-step explanation:

ab is a tangent drawn from an point b to a circle with centre c

=> Δcab is a right angle triangle

∠cab = 90 ° ( Tangent)

∠cba = 30°  given

Sin∠cba = ca /cb

ca = Radius = 1.5 cm

=> Sin30°  = ca /cb

=> 1/2  = 1.5 /cb

=> cb = 3 cm

ab² = cb² - ca²

=> ab² = 3² - 1.5²

=> ab²  = 1.5²(4 - 1)

=> ab² = 1.5² * 3

=> ab = 1.5√3

=> ab = 3√3/2 cm

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Answer 2

Step-by-step explanation:

GIVEN:-

AP Is a tangent to a circle with centre C

angle ACP = 30°

TO FIND:-

Length of AP

CONSTRUCTION:-

Let us join C to P

SOLUTION:-

In triangle ACP

tan C = AP/AC

30° = AP/1.5

AP= 45 cm

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