Question

Construct two tangents ab and ac from an external point a to a circle of radius 3.5cm and center o such that angle boc=105 degree and measure the length of tangents

Answer 1

Answer:

i don't know

Answer 2

The lengths of tangents of the circle = 4.56 cm

Step-by-step explanation:

From the figure OCAB is the quadi lateral.& the sum of opposite angles of quadilateral is = 180°

⇒ ∠ B O C + ∠ B A C = 180°

⇒ 105° + ∠ B A C = 180°

⇒ ∠ B A C = 75°

From the Δ A B O. Apply sine rule we get,

$\frac{OB}{\sin37.5} = \frac{AB}{\sin 52.5}$

OB = 3.5 cm = radius of circle.

$\frac{3.5}{\sin 37.5} = \frac{AB}{\sin 52.5}$

AB = 4.56 cm

This is the first tangent of the circle.

Similarily from the triangle O A C

$\frac{OC}{\sin37.5} = \frac{AC}{\sin52.5}$

$\frac{3.5}{\sin37.5} = \frac{AC}{\sin52.5}$

AC = 4.56

This is the second tangent of the circle.