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In a circle with center O and radius 13 cm, a chord AB is drawn. Tangents at A and B intersects at P such that ∠APB = 60°. If the distance of AB from the center O is 5 cm, then what is the length (in cm) of AP?

In a circle with center O and radius 13 cm, a chord AB is drawn. Tangents at A and B intersects at P such that ∠APB = 60°. If the distance of AB from the center O is 5 cm, then what is the length (in cm) of AP? Correct Answer 24

Given:

Radius = 13 cm

∠APB = 60°

Distance of AB from the centre O is 5 cm

Concept used:

If from one external point, two tangents are drawn to a circle then they have equal tangent segments.

Calculation:

Additional InformationCriteria for Similarity of Triangles:

Angle–Angle–Angle: If in two triangles, corresponding angles are

equal, then their corresponding sides are in the same ratio (or

proportion) and hence the two triangles are similar.

SSS (Side–Side–Side): If in two triangles, sides of one triangle are

proportional to the sides of the other triangle, then their corresponding

angles are equal and hence the two triangles are similar.

SAS (Side–Angle–Side):  If one angle of a triangle is equal to one

angle of the other triangle and the sides including these angles are

proportional, then the two triangles are similar.

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