Question

In the given figure, 'O' is the centre of circle. If AB = 6 cm and AC = 5 cm then the product of AO and AX is:
(a) 15
(b) 20
(c) 25
(d) 30

Answer 1

ANSWER ✔✔

O is the center.

•°• angle ACE = 90° [°•° angle in a semicircle]

In tri. ACE and tri. AXB,

angle ACE = angle AXB = 90

angle AEC = angle ABX

[ °•° angle subtended by the same arc]

•°• tri. ACE ~ tri. AXB [ AA similarity]

So,

$\frac{ac}{ax} = \frac{ce}{xb} = \frac{ae}{ab}$

Since AE is the diameter, so AE = 2AO

$\frac{ac}{ax} = \frac{ae}{ab}$

AC / AX = 2AO/AB

》5 / AX = 2AO / 6

[AB=6 AC = 5]

》5 × 6 = AX × 2AO

》30 / 2 = AX × AO

》15 = AX × AO

THEREFORE, 15 IS THE CORRECT ANSWER.

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