Find the length of the tangent

Geometry Level 5

ABC is an acute angle triangle with side AC=10cm. A perpendicular is drawn from point A on side BC that cuts the side BC at point D. Length of AD=6cm. \(\angle BAD=30°\). Then two tangents are drawn from points B and C to the circumcircle of ΔACD &ΔABD respectively. Consider those two tangents are BT&CS respectively. Then find the ratio of \[\frac{BT×CS}{BC}\]

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