Question

In the given figure, AB is a tangent to a
circle with centre ‘O'. Find OA, OB and AB.

Answer 1

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Answer 2

In ∆OAB, angle OAB = 90° ... (radius _|_ tangent)

OA² + AB² = OB² ... (Pythagorean theorem)

x² + (x + 2)² = (x + 4)²

x² + x² + 4x + 4 = x² + 8x + 16

2x² - x² + 4x - 8x + 4 - 16 = 0

x² - 4x - 12 = 0

x² - 6x + 2x - 12 = 0

x(x - 6) + 2(x - 6) = 0

(x + 2)(x - 6) = 0

x + 2 = 0 or x - 6 = 0

x = -2 or x = 6

but, since x is the measure of length of radius OA, it can't be negative.

Hence, x ≠ -2 in this case.

Hence, x = 6

hence, measure of the sides–

0A = x = 6 cm

AB = x + 2 = 8 cm

OB = x + 4 = 10 cm

Hence, measures of sides of ∆OAB are 6cm, 8 cm, and 10cm.