Question

In the addjoing figure cricle with center x and y touch each other at point z A secant ​

Answer 1

Explanation:

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Construction: Draw segments XZ and YZ.

Proof: By theorem of touching circles, points X, Z, Y are collinear.

∴∠XZA≅∠BZY (opposite angles)

Let ∠XZA=∠BZY=a.....(I)

Now, segXA≅segXZ........(Radii of circle with centre X)

∴∠XAZ=∠XZA=a......(isosceles triangle theorem) (II)

Similarly, segYB≅segYZ.......(Radii of circle with centre Y)

∴∠BZY=∠ZBY=a.....(isosceles triangle theorem) (Ill)

∴from(I),(II),(Ill),

∠XAZ=∠ZBY

∴radiusXAIlradiusYZ......(Alternate angle test)

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