A tangent AB (B-point of tangency) and a secant line are drawn through point A, which intersects

univerkov | September 6, 2021 | education

A tangent AB (B-point of tangency) and a secant line are drawn through point A, which intersects the circle at points C and D. Find CD if: a) AB = 4cm AC = 2cm b) AB = 5cm AD = 10cm

By the property of the tangent to the circle and the secant, coming out of one point, the square of the distance from this point to the point of tangency is equal to the product of the length of the secant by the length of its outer part.

AB ^ 2 = AD * AC.

A) 4 ^ 2 = AD * 2.

AD = 16/2 = 8 cm.

Then СD = АD – АС = 8 – 2 = 6 cm.

Answer: CD = 6 cm.

B) 52 = 10 * AC.

AC = 25/10 = 2.5 cm.

CD = AD – AC = 10 – 2.5 = 7.5 cm.

Answer: СD = 7.5 cm.

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