Saved Bookmarks
| 1. |
25. In figure, the sides AB, BC and CA of triangle ABC touch a circle-with centre Oand radius r at P. O and R respectivelyProve that:(i) Area (AABQ(Perimeter of A4BC)xiah other on either side |
|
Answer» Since the lengths of tangents drawn from an exterior point to a circle are equal.∴ AP = AR , BP = BQ, CQ = CRNow, AB+CQ = AP+PB+CQ = AR+BQ+CQ (∵ AP=AR and PB=BQ) =(AR+CR)+BQ (∵CQ=CR) = AC+BQ∴ AB+ CQ = AC+BQ Area (tri . ABC) = Area (tri .AOB) + Area (tri .BOC) + Area (tri . COA) = 1/2 AB x r + 1/2 BC x r + 1/2 CA x r = 1/2 r (AB + BC + CA) -= 1/2 r ( perimeter of triangle ABC ) Like my answer if you find it useful! |
|