A tangent AC and AB are drawn to a circle from a point A , such that angle BAC = - Maths - Circles

Question

A tangent AC and AB are drawn to a circle from a point A ,
such that angle BAC = 30o A chord BD is drawn parallel
to the tangent AC find angle DBC

Koka Sri Lakshmi Divya Sai · Accepted Answer

$Draw a line through C and ⊥ to AB \Rightarrow If a line ⊥ to tangent,then it must be passed th rough the center of circle (∵ radius and tangent are ⊥ to each other at the point of contact) \Rightarrow AC=AB ∵ from an external point the length of tangents are equal In Δ ACB AC=AB by isosceles triangle property \Rightarrow ∠ C = ∠ B \Rightarrow ∠ A+ ∠ B+ ∠ C= 180^{0} \Rightarrow 30^{0} + ∠ C+ ∠ {C=180}^{0} \Rightarrow 2 ∠ {C=150}^{0} \Rightarrow ∠ {C=75}^{0} ∠ ACB= ∠ {CDB=75}^{0} (alternate segment theorem) ∠ ACB= ∠ {CBD=75}^{0} (∵ BD ∥ AC alternate interior angle) ∴ ∠ {DBC=75}^{0}$

A tangent AC and AB are drawn to a circle from a point A , such that angle BAC = 30o. A chord BD is drawn parallel to the tangent AC. find angle DBC.

A tangent AC and AB are drawn to a circle from a point A , such that angle BAC = 30^o. A chord BD is drawn parallel to the tangent AC. find angle DBC.