Multiple choice

If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that ${\angle DBC = 120^0}$, then BC + BD = BO, i.e., BO = 2BC

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a circle, the tangents from an external point are equal. If angle DBC = 120, the triangle formed by the center and the tangents allows calculating the side lengths using trigonometry. The statement BO = 2BC is correct.

AI explanation

Since BC and BD are tangents from external point B, the line BO bisects angle DBC, making angle CBO equal to 60 degrees. The radius OC is perpendicular to tangent BC, creating a right-angled triangle OCB with angles of 30, 60, and 90 degrees. In a 30-60-90 triangle, the hypotenuse BO is twice the length of the side opposite the 30-degree angle, BC. This confirms that BC plus BD equals BO because the tangents BC and BD are equal in length and their individual sum is 2BC, making the statement true.

Keep practicing — related questions