From one point, two tangents are drawn to the circle, the length of each of which is 156 cm.

| April 25, 2021 | education

From one point, two tangents are drawn to the circle, the length of each of which is 156 cm. Find the radius of the circle if the distance between the points of contact is 120 cm

Let us construct a segment OA, which is the bisector of the angle BAC and is perpendicular to the segment BC.

Then In an isosceles triangle BAC, the height of AH is also its median, then BH = CH = 120/2 = 60 cm.

In a right-angled triangle ABH, SinBAH = BH / AB = 60/156 = 5/13.

Then CosBAH = √ (1 – 25/169) = 12/13.

The radius of the circle drawn to the tangent is perpendicular to the tangent, then AOB is a right-angled triangle, and BH is the height drawn to the hypotenuse. Then the triangle AOB is similar to the triangle OBH, and then CosOBH = CosBAH = 12/13.

In a right-angled triangle BOH, CosOBH = BH / OB.

OB = BH / CosOBH = 60 / (12/13) = 60 * 13/12 = 65 cm.

Answer: The radius of the circle is 65 cm.



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