Q. 175.0( 3 Votes )

# AP and PQ are tan

Answer :

Given:

Radius = 9 cm

OA = 15 cm

Property 1: If two tangents are drawn to a circle from one external point, then their tangent segments (lines joining the external point and the points of tangency on circle) are equal.

By the above property,

AP = AQ (tangent from A)

Property 2: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.

By above property, ∆POA is right-angled at OAP (i.e., OPA = 90°).

Therefore by Pythagoras theorem,

AP2 + PO2 = AO2

AP2 = AO2 – PO2

AP2 = 152 – 92

AP2 = 225 – 81

AP2 = 144

AP = 144

AP = 12

AP + AQ = 12 cm + 12 cm = 24 cm

Hence, AP + AQ = 24 cm

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