A secant is drawn from a point P to a circle so that it meets the circle first at A then goes ...........

Quantitative Aptitude (CHSL) Geometry

A secant is drawn from a point P to a circle so that it meets the circle first at A, then goes through the centre, and leaves the circle at B. If the length of the tangent from P to the circle is 12 cm, and the radius of the circle is 5 cm, then the distance from P to A is:

10 cm

8 cm

12 cm

18 cm

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Explanation:

Correct option:2

Let the value of PA be X
The tangent PT is perpendicular to OT
By Pythagoras theorem, (PO)² =(PT)² + (OT)²
PO = PA + OA = X + 5
substituting the value in the formula (PO)² = 12² + 5²

(PO)² = 144 + 25
PO = 13 cm
X + 5 = 13
PA = X = 8 cm

Hence The distance from P to A is 8 cm.