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Chapter 9: Q15. (page 342)

a. Given:WZ炉is a diameter of 鈯�O;

Prove: m鈭�Z=n.

Short Answer

Expert verified

The final answer is m鈭�Z=n.

Step by step solution

01

Step 1. Given information:

WZ炉 is a diameter of circle and m(WX)=m(XY)=n

02

Step 2. Concept used:

We use basic geometric and angle concept

03

Step 3. Applying the concept:

First let us draw OY炉 in the given figure.

Then OY炉and OZ炉 becomes radii of the circles 鈬�OY炉=OZ炉

Since mXY=m鈭�XOY=n

Since OX炉鈥�||ZY炉鈥�and OY炉 transverse line

鈬�m鈭�XOY=m鈭�OYZ=鈥�n

and also 螖鈥�OZY is isosceles triangles as OY炉=OZ炉 then m鈭�OYZ鈥�鈥�=m鈭�OZY=n

Hence, m鈭�Z鈥�鈥�=n

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