Chord AB of circle of radius 10 cm is at a distance 8 cm from the centre O If tangents drawn at A an...........

Quantitative Aptitude (CGL) Geometry

Chord AB of circle of radius 10 cm is at a distance 8 cm from the centre O. If tangents drawn at A and B intersect at P, then the length of the tangent AP (in cm) is:

This questions was previously asked in

SSC CGL 18th August 2021 Shift-1

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7.5

3.75

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Explanation:

Correct option 1: 7.5

Given Radius =10 cm

AAA(Angle, Angle, Angle similarity → If all three angles in one triangle are the same as the corresponding angles in the other, then the triangles are similar.

In, the given figure,
ADAO ~ AAPO [OAP = ODA = 90° and AOD is common in two triangles]
AD/AP = DO/AO
⇒6/AP = 8/10 [6, 8, 10 pythagoras triplets]
⇒ AP = 60/8
⇒ AP = 7.5 cm
Length of tangent AP is 7.5 cm