Question

PQ is tangent to a circle with centre O. If OQ = a, OP = a + 2 and PQ = 2b, then relation between a and b is

Options

• a² + (a + 2)² = (2b)²

• b² = a + 4

• 2a² + 1 = b²

• b² = a + 1

Answer 1

b² = a + 1

Explanation:

Given:

OQ = a

PQ = 2b

OP = a + 2

Applying Pythagoras Theorem:

OQ² + PQ² = OP²

a² + (2b)² = (a + 2)²

a² + 4b² = a² + 4a + 4

4b² = 4a + 4

b² = a + 1

The relation between a and b is b² = a + 1.