SOLUTION: In a diagram below PQR is a semi-circle with diameter 20cm,if PQ=16cm and QR=12cm. caculate, correct to the neares whole number. (i) the radius of the circle (ii) the area of the

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Question 1028887: In a diagram below PQR is a semi-circle with diameter 20cm,if PQ=16cm and QR=12cm. caculate, correct to the neares whole number.
(i) the radius of the circle
(ii) the area of the shaded part
Answer by mathmate(429) (Show Source):
You can put this solution on YOUR website!

Question:
In a diagram below PQR is a semi-circle with diameter 20cm,if PQ=16cm and QR=12cm. caculate, correct to the neares whole number.
(i) the radius of the circle
(ii) the area of the shaded part

Solution:
There is no attached diagram. From the context, I have recreated the diagram below. Hope this is the problem you intended.

Here I assume the given lengths are chord lengths (as opposed to arc lengths).
So mPQ=16, mQR=12 cm. (point Q should have been drawn to the right of O.)
Since angles subtended by diameters are right angles, we have a right-angled triangle PQR right-angled at Q.
Using Pythagoras theorem, we have
PR²=PQ²+QR²=16²+12²=256+144=400
Hence
diameter=PR=√400=20.