AB is tangent to circle O if AO = 30 and bc = 48. What is AB

Solution:

Given, AB is tangent to circle O.

AO = 30 units

BC = 48 units.

We have to find AB.

From the figure,

AO = CO = radius of the circle

So, BO = BC + CO

= BC + AO

= 48 + 30

BO = 78 units

Now, ABO is a triangle right angled at A.

By Pythagorean Theorem,

AB² + AO² = BO²

AB² + (30)² = (78)²

AB² + 900 = 6084

AB² = 6084 - 900

AB² = 5184

Taking square root,

AB = 72 units.

Therefore, AB is 72 units.

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AB is tangent to circle O if AO = 30 and bc = 48. What is AB

Summary:

AB is tangent to circle O if AO = 30 and bc = 48, then AB = 72.