In the figure, O is the centre of a circle of radius 29 cm. OT ⊥ AB, OQ ⊥ CD and AB is parallel CD. If AB = 40 cm and CD = 42 cm, then the length of PQ is:
Answer & explanation
Correct answer: option 3
We know that,
(hypotenuse) 2 = (perpendicular)2 + (base)2
We have,
If,
AB= 40 cm, CD = 42 cm
then, AP = 20 cm,
CQ = 21 cm.
In right angled triangle APO and OQC
Pythagoras theorem;
OA2 = OP2 + PA2
292 = OP2 + 202
841 = OP2 + 400
0P2 = 441
OP = 21 cm.
also,
OC2 = OQ2 + CQ2
292 = OQ2 + 212
841 = OQ2 + 441
OQ2 = 400
OQ = 20 cm.
PQ = OP + OQ = 21 + 20 = 41 cm