Question

As shown in the figure, AP is the tangent to the circle at point A. Secant through P intersects chord AY in point X, such that AP=PX=XY. If PQ=1 and QZ=8; then find AX.

Answer 1

ANSWER:-

Given:

In fig. AP is the tangent to the circle at point A. Sacant through P intersects chord AY in point X, such that AP=PX=XY.

If PQ= 1cm & QZ= 8cm.

To find:

Find AX.

Solution:

According to the tangent.

Using Secant Theorem:

PQ × PZ = PA²

=) PQ[PQ + QZ] = PA²

=) 1(1+8)= PA²

=) 1(9)= PA²

=) PA² = 9

=) PA² = 3²

=) PA= 3cm

So,

PA = PX = XY = 3cm

Now,

PX = 3cm

=) PQ + QX= 3

=) 1 + QX = 3

=) QX= 3-1

=) QX= 2cm

Now,

QZ = 8cm

=) ZX + QX = 8

=) ZX + 2 = 8

=) ZX = 8-2

=) ZX = 6cm

We know that when two chords of a circle intersect internally, then product of the length of segments are equal.

So,

AX × XY = ZX × QX

=) AX × 3 = 6 × 2

=) 3AX = 12

=) AX= 12/3

=) AX = 4cm

Thus,

AX is the required of 4cm.

Hope it helps ☺️

Answer 2

Step-by-step explanation:

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