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:

41 cm

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