2026 · Q65
Let O be the centre of a circle. Let the chords AB = 10 cm and CD = 24 cm be two parallel chords of the circle. The two chords are on opposite side of the centre and the distance between them is 17 cm. Let P be the midpoint of AB, and Q be the midpoint of CD. Further, the points O and A, the points O and C, the points A and C are joined. Which of the statements given below is/are correct?
- IArea of triangle OAP is equal to area of triangle OCQ.
- IIArea of triangle OAC is equal to 102 cm². Select the answer using the code given below:
Elementary MathematicsCircles
- AI only
- BII only
- CBoth I and II
- DNeither I nor II
Explanation
Put OP=d1, OQ=d2: d1+d2=17 and r²=25+d1²=144+d2², giving d1−d2=7, hence d1=12, d2=5. Area(ΔOAP)=¹⁄₂·12·5=30=¹⁄₂·5·12=area(ΔOCQ), so I is correct. The area of ΔOAC works out to 84.5 or 59.5 cm² (depending on the side), never 102, so II is incorrect. Only I is correct, option A.