Question

AB is a tangent to a circle with centre P touching the circle at B . PA intersects the circle at B . If AB=35 cm and AM=25 cm, find the diameter of the circle.

Answer 1

Answer:

diameter ten centimeters

Answer 2

The diameter of the circle is 24 cm

Step-by-step explanation:

AB is a tangent to a circle with center P touching the circle at B

Please see the attachment for figure.

Let the diameter of circle be d cm

PA intersects the circle at M. If AB=35 cm and AM=25 cm

Using PT²  theorem: (If PAB is a secant to a circle intersecting it at A and B and PT is a tangent then PA.PB = PT²)

$AB^2=AM\cdot AN$

$35^2=25\cdot (25+d)$

$25+d=\dfrac{1225}{25}=49$

$d=49-25$

$d=24$

Hence, the diameter of the circle is 24 cm

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