CBSE Class 10 Maths (Standard) 2022 · Paper 30/1/1 · Question 12

Circles 4 marks Hard

In Figure 1, a triangle ABC with

∠ B = 9 0^{\circ}

is shown. Taking AB as diameter, a circle has been drawn intersecting AC at point P. Prove that the tangent drawn at point P bisects BC.

Figure 1: right triangle ABC with circle on AB as diameter meeting AC at P; tangent at P meets BC at Q.

Answer

QB = QC, so the tangent at P bisects BC. (Proved.)

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