A circle touches two adjacent sides of a rectangle AB and AD at Points P and - Maths - Coordinate Geometry

Question

A circle touches two adjacent sides of a rectangle AB and AD at
Points P and Q respectively Third vertex C of the rectangle lies on
the circle The length of perpendicular from vertex C to the chord
PQ is 5 Find the area of rectangle

Brijendra Pal · Accepted Answer

Dear Student, Let C lie on the arc Câ‚Câ‚‚ Label the 90° and 45° angles

Since PQ subtends a central angle of 90°, the inscribed angle PCQ must be 45°

Let ∠BCP = α Label the remaining angles in terms of α:

Draw the perpendicular from C to PQ Let E be the point of intersection ∠ECQ = α ∠PCE = 45-α

Since EC = 5 and ∠ECQ = α, CQ = 5/cosα Since ∠QCD = 45-α, CQ = CD/cos(45-α) 5/cosα = CD/cos(45-α) CD = 5·cos(45-α)/cosα Similarly, BC = 5·cosα/cos(45-α) Area of rectangle ABCD = CD×BC = 25 square units Regards

A circle touches two adjacent sides of a rectangle AB and AD at Points P and Q respectively. Third vertex C of the rectangle lies on the circle . The length of perpendicular from vertex C to the chord PQ is 5. Find the area of rectangle..