If ab is a tangent drawn from an point b to a circle with centre c qnd radius 1.5 cm sucb that angle cba=30 degree then find the length of tangent ab and line cb
Answers
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:
AB = 3cm
BC = 3√3/2 cm
Step-by-step explanation:
Ab is a tangent with B as a exterior point C as centre and AC as radius
Sin30° = AC/AB
1/2 = 1.5/AB
AB = 3cm
tan30° = AC/BC
1/√3 = 1.5/BC
BC = 1.5/√3
3√3/2 cm